# Hailstone sequence

Hailstone sequence
You are encouraged to solve this task according to the task description, using any language you may know.

The Hailstone sequence of numbers can be generated from a starting positive integer,   n   by:

•   If   n   is     1     then the sequence ends.
•   If   n   is   even then the next   n   of the sequence    = n/2
•   If   n   is   odd   then the next   n   of the sequence    = (3 * n) + 1

The (unproven) Collatz conjecture is that the hailstone sequence for any starting number always terminates.

The hailstone sequence is also known as   hailstone numbers   (because the values are usually subject to multiple descents and ascents like hailstones in a cloud).

This sequence is also known as the   Collatz sequence.

1. Create a routine to generate the hailstone sequence for a number.
2. Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1
3. Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.
(But don't show the actual sequence!)

•   xkcd (humourous).

## 360 Assembly

*        Hailstone sequence        16/08/2015HAILSTON CSECT         USING  HAILSTON,R12         LR     R12,R15         ST     R14,SAVER14BEGIN    L      R11,=F'100000'     nmax         LA     R8,27              n=27         LR     R1,R8         MVI    FTAB,X'01'         ftab=true         BAL    R14,COLLATZ         LR     R10,R1             p         XDECO  R8,XDEC            n         MVC    BUF1+10(6),XDEC+6         XDECO  R10,XDEC           p         MVC    BUF1+18(5),XDEC+7         LA     R5,6         LA     R3,0               i         LA     R4,BUF1+25LOOPED   L      R2,TAB(R3)         tab(i)         XDECO  R2,XDEC         MVC    0(7,R4),XDEC+5         LA     R3,4(R3)           i=i+1         LA     R4,7(R4)         C      R5,=F'4'         BNE    BCT         LA     R4,7(R4) BCT      BCT    R5,LOOPED         XPRNT  BUF1,80            print hailstone(n)=p,tab(*)         MVC    LONGEST,=F'0'      longest=0         MVI    FTAB,X'00'         ftab=true         LA     R8,1               iLOOPI    CR     R8,R11             do i=1 to nmax         BH     ELOOPI         LR     R1,R8              n         BAL    R14,COLLATZ         LR     R10,R1             p         L      R4,LONGEST         CR     R4,R10             if longest<p         BNL    NOTSUP         ST     R8,IVAL            ival=i         ST     R10,LONGEST        longest=pNOTSUP   LA     R8,1(R8)           i=i+1         B      LOOPIELOOPI   EQU    *                  end i         XDECO  R11,XDEC           maxn         MVC    BUF2+9(6),XDEC+6         L      R1,IVAL            ival         XDECO  R1,XDEC         MVC    BUF2+28(6),XDEC+6         L      R1,LONGEST         longest         XDECO  R1,XDEC         MVC    BUF2+36(5),XDEC+7         XPRNT  BUF2,80            print maxn,hailstone(ival)=longest         B      RETURN*        *      *                  r1=collatz(r1)COLLATZ  LR     R7,R1              m=n  (R7)         LA     R6,1               p=1  (R6)LOOPP    C      R7,=F'1'           do p=1 by 1 while(m>1)         BNH    ELOOPP         CLI    FTAB,X'01'         if ftab         BNE    NONOK         C      R6,=F'1'           if p>=1         BL     NONOK         C      R6,=F'3'           & p<=3         BH     NONOK         LR     R1,R6              then         BCTR   R1,0         SLA    R1,2         ST     R7,TAB(R1)         tab(p)=mNONOK    LR     R4,R7              m         N      R4,=F'1'           m&1         LTR    R4,R4              if m//2=0  (if not(m&1))         BNZ    ODDEVEN     SRA    R7,1               m=m/2         B      EIFMODD      LA     R3,3         MR     R2,R7              *m         LA     R7,1(R3)           m=m*3+1EIFM     CLI    FTAB,X'01'         if ftab         BNE    NEXTP         MVC    TAB+12,TAB+16      tab(4)=tab(5)         MVC    TAB+16,TAB+20      tab(5)=tab(6)         ST     R7,TAB+20          tab(6)=mNEXTP    LA     R6,1(R6)           p=p+1         B      LOOPPELOOPP   LR     R1,R6              end p; return(p)         BR     R14                end collatz*                RETURN   L      R14,SAVER14        restore caller address         XR     R15,R15            set return code         BR     R14                return to callerSAVER14  DS     FIVAL     DS     FLONGEST  DS     FN        DS     FTAB      DS     6FFTAB     DS     XBUF1     DC     CL80'hailstone(nnnnnn)=nnnnn : nnnnnn nnnnnn nnnnnn ...*               ... nnnnnn nnnnnn nnnnnn'BUF2     DC     CL80'longest <nnnnnn : hailstone(nnnnnn)=nnnnn'XDEC     DS     CL12         YREGS         END    HAILSTON
Output:
hailstone(    27)=  112 :     27     82     41 ......      4      2      1
longest <100000 : hailstone( 77031)=  351


## ABAP

 CLASS lcl_hailstone DEFINITION.  PUBLIC SECTION.    TYPES: tty_sequence TYPE STANDARD TABLE OF i                             WITH NON-UNIQUE EMPTY KEY,           BEGIN OF ty_seq_len,             start TYPE i,             len   TYPE i,           END OF ty_seq_len,           tty_seq_len TYPE HASHED TABLE OF ty_seq_len                            WITH UNIQUE KEY start.     CLASS-METHODS:      get_next        IMPORTING          n                           TYPE i        RETURNING          VALUE(r_next_hailstone_num) TYPE i,       get_sequence        IMPORTING          start             TYPE i        RETURNING          VALUE(r_sequence) TYPE tty_sequence,       get_longest_sequence_upto        IMPORTING          limit                     TYPE i        RETURNING          VALUE(r_longest_sequence) TYPE ty_seq_len.   PRIVATE SECTION.    TYPES: BEGIN OF ty_seq,             start TYPE i,             seq   TYPE tty_sequence,           END OF ty_seq.    CLASS-DATA: sequence_buffer TYPE HASHED TABLE OF ty_seq                                     WITH UNIQUE KEY start.ENDCLASS. CLASS lcl_hailstone IMPLEMENTATION.  METHOD get_next.    r_next_hailstone_num = COND #( WHEN n MOD 2 = 0 THEN n / 2                                   ELSE ( 3 * n ) + 1 ).  ENDMETHOD.   METHOD get_sequence.    INSERT start INTO TABLE r_sequence.    IF start = 1.      RETURN.    ENDIF.     READ TABLE sequence_buffer ASSIGNING FIELD-SYMBOL(<buff>)                               WITH TABLE KEY start = start.    IF sy-subrc = 0.      INSERT LINES OF <buff>-seq INTO TABLE r_sequence.    ELSE.      DATA(seq) = get_sequence( get_next( start ) ).      INSERT LINES OF seq INTO TABLE r_sequence.      INSERT VALUE ty_seq( start = start                           seq   = seq ) INTO TABLE sequence_buffer.    ENDIF.  ENDMETHOD.   METHOD get_longest_sequence_upto.    DATA: max_seq TYPE ty_seq_len,          act_seq TYPE ty_seq_len.     DO limit TIMES.      act_seq-len = lines( get_sequence( sy-index ) ).       IF act_seq-len > max_seq-len.        max_seq-len   = act_seq-len.        max_seq-start = sy-index.      ENDIF.    ENDDO.     r_longest_sequence = max_seq.  ENDMETHOD.ENDCLASS. START-OF-SELECTION.  cl_demo_output=>begin_section( |Hailstone sequence of 27 is: | ).  cl_demo_output=>write( REDUCE string( INIT result =                                         FOR item IN lcl_hailstone=>get_sequence( 27 )                                        NEXT result = |{ result } { item }| ) ).  cl_demo_output=>write( |With length: { lines( lcl_hailstone=>get_sequence( 27 ) ) }| ).  cl_demo_output=>begin_section( |Longest hailstone sequence upto 100k| ).  cl_demo_output=>write( lcl_hailstone=>get_longest_sequence_upto( 100000 ) ).  cl_demo_output=>display( ).
Output:
Hailstone sequence of 27 is:

27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1

With length: 112

Longest hailstone sequence upto 100k

Structure
START LEN
77031 351



## ACL2

(defun hailstone (len)    (loop for x = len              then (if (evenp x)                          (/ x 2)                          (+ 1 (* 3 x)))         collect x until (= x 1))) ;; Must be tail recursive(defun max-hailstone-start (limit mx curr)   (declare (xargs :mode :program))   (if (zp limit)       (mv mx curr)       (let ((new-mx (len (hailstone limit))))          (if (> new-mx mx)              (max-hailstone-start (1- limit) new-mx limit)              (max-hailstone-start (1- limit) mx curr)))))
Output:
> (take 4 (hailstone 27))
(27 82 41 124)
> (nthcdr 108 (hailstone 27))
(8 4 2 1)
> (len (hailstone 27))
112
> (max-hailstone-start 100000 0 0)
(351 77031)

Similar to C method:

with Ada.Text_IO; use Ada.Text_IO;procedure hailstone is	type int_arr is array(Positive range <>) of Integer;	type int_arr_pt is access all int_arr; 	function hailstones(num:Integer; pt:int_arr_pt) return Integer is		stones : Integer := 1;		n : Integer := num;		begin		if pt /= null then pt(1) := num; end if;		while (n/=1) loop			stones := stones + 1;			if n mod 2 = 0 then n := n/2;			else n := (3*n)+1;			end if;			if pt /= null then pt(stones) := n; end if;		end loop;		return stones;	end hailstones; 	nmax,stonemax,stones : Integer := 0;	list : int_arr_pt;begin	stones := hailstones(27,null);	list := new int_arr(1..stones);	stones := hailstones(27,list);	put(" 27: "&Integer'Image(stones)); new_line;	for n in 1..4 loop put(Integer'Image(list(n)));	end loop;	put(" .... ");	for n in stones-3..stones loop put(Integer'Image(list(n))); end loop;	new_line;	for n in 1..100000 loop		stones := hailstones(n,null);		if stones>stonemax then			nmax := n; stonemax := stones;		end if;	end loop;	put_line(Integer'Image(nmax)&" max @ n= "&Integer'Image(stonemax));end hailstone;
Output:
 27:  112
27 82 41 124 ....  8 4 2 1
77031 max @ n=  351


### Alternative method

A method without pointers or dynamic memory allocation, but slower for simply counting. This is also used for the "executable library" task Executable library#Ada.

package Hailstones is   type Integer_Sequence is array(Positive range <>) of Integer;   function Create_Sequence (N : Positive) return Integer_Sequence;end Hailstones;

package body Hailstones is   function Create_Sequence (N : Positive) return Integer_Sequence is   begin      if N = 1 then         -- terminate         return (1 => N);      elsif N mod 2 = 0 then         -- even         return (1 => N) & Create_Sequence (N / 2);      else         -- odd         return (1 => N) & Create_Sequence (3 * N + 1);      end if;   end Create_Sequence;end Hailstones;

with Ada.Text_IO;with Hailstones; procedure Main is   package Integer_IO is new Ada.Text_IO.Integer_IO (Integer);    procedure Print_Sequence (X : Hailstones.Integer_Sequence) is   begin      for I in X'Range loop         Integer_IO.Put (Item => X (I), Width => 0);         if I < X'Last then            Ada.Text_IO.Put (", ");         end if;      end loop;      Ada.Text_IO.New_Line;   end Print_Sequence;    Hailstone_27 : constant Hailstones.Integer_Sequence :=     Hailstones.Create_Sequence (N => 27); begin   Ada.Text_IO.Put_Line ("Length of 27:" & Integer'Image (Hailstone_27'Length));   Ada.Text_IO.Put ("First four: ");   Print_Sequence (Hailstone_27 (Hailstone_27'First .. Hailstone_27'First + 3));   Ada.Text_IO.Put ("Last four: ");   Print_Sequence (Hailstone_27 (Hailstone_27'Last - 3 .. Hailstone_27'Last));    declare      Longest_Length : Natural := 0;      Longest_N      : Positive;      Length         : Natural;   begin      for I in 1 .. 99_999 loop         Length := Hailstones.Create_Sequence (N => I)'Length;         if Length > Longest_Length then            Longest_Length := Length;            Longest_N := I;         end if;      end loop;      Ada.Text_IO.Put_Line ("Longest length is" & Integer'Image (Longest_Length));      Ada.Text_IO.Put_Line ("with N =" & Integer'Image (Longest_N));   end;end Main;
Output:
Length of 27: 112
First four: 27, 82, 41, 124
Last four: 8, 4, 2, 1
Longest length is 351
with N = 77031

## Aime

voidprint_hailstone(integer h){    list l;     while (h ^ 1) {        lb_p_integer(l, h);        h = h & 1 ? 3 * h + 1 : h / 2;    }     o_form("hailstone sequence for ~ is ~1 ~ ~ ~ .. ~ ~ ~ ~, it is ~ long\n",           l[0], l[1], l[2], l[3], l[-3], l[-2], l[-1], 1, ~l + 1);} voidmax_hailstone(integer x){    integer e, i, m;    index r;     m = 0;    i = 1;    while (i < x) {        integer h, k, l;         h = i;        l = 1;        while (h ^ 1) {            if (i_j_integer(k, r, h)) {                l += k;                break;            } else {                l += 1;                h = h & 1 ? 3 * h + 1 : h / 2;            }        }         r[i] = l - 1;         if (m < l) {            m = l;            e = i;        }         i += 1;    }     o_form("hailstone sequence length for ~ is ~\n", e, m);} integermain(void){    print_hailstone(27);    max_hailstone(100000);     return 0;}
Output:
hailstone sequence for 27 is 27 82 41 124 .. 8 4 2 1, it is 112 long
hailstone sequence length for 77031 is 351

## ALGOL 68

Translation of: C
- note: This specimen retains the original C coding style.
Works with: ALGOL 68 version Standard - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - using the print routine rather than printf
MODE LINT = # LONG ... # INT; PROC hailstone = (INT in n, REF[]LINT array)INT:(    INT hs := 1;    INT index := 0;    LINT n := in n;     WHILE n /= 1 DO        hs +:= 1;        IF array ISNT REF[]LINT(NIL) THEN array[index +:= 1] := n FI;        n := IF ODD n THEN 3*n+1 ELSE n OVER 2 FI    OD;    IF array ISNT REF[]LINT(NIL) THEN array[index +:= 1] := n FI;    hs); main:(    INT j, hmax := 0;    INT jatmax, n;    INT border = 4;     FOR j TO 100000-1 DO        n := hailstone(j, NIL);       IF hmax < n THEN           hmax := n;           jatmax := j       FI    OD;     [2]INT test := (27, jatmax);    FOR key TO UPB test DO        INT val = test[key];        n := hailstone(val, NIL);        [n]LINT array;        n := hailstone(val, array);         printf(($"[ "n(border)(g(0)", ")" ..."n(border)(", "g(0))"] len="g(0)l$,            array[:border], array[n-border+1:], n))        #;free(array) #    OD;    printf(($"Max "g(0)" at j="g(0)l$, hmax, jatmax))# ELLA Algol68RS:    print(("Max",hmax," at j=",jatmax, new line))#)
Output:
[ 27, 82, 41, 124,  ..., 8, 4, 2, 1] len=112
[ 77031, 231094, 115547, 346642,  ..., 8, 4, 2, 1] len=351
Max 351 at j=77031


## ALGOL W

begin    % show some Hailstone Sequence related information                       %    % calculates the length of the sequence generated by n,                  %    % if showFirstAndLast is true, the first and last 4 elements of the      %    % sequence are stored in first and last                                  %    % hs holds a cache of the upbHs previously calculated sequence lengths   %    % if showFirstAndLast is false, the cache will be used                   %    procedure hailstone ( integer value  n                        ; integer array  first, last ( * )                        ; integer result length                        ; integer array  hs          ( * )                        ; integer value  upbHs                        ; logical value  showFirstAndLast                        ) ;    if not showFirstAndLast and n <= upbHs and hs( n ) not = 0 then begin        % no need to store the start and end of the sequence and we already  %        % know the length of the sequence for n                              %        length := hs( n )        end    else begin        % must calculate the sequence length                                 %        integer sv;        for i := 1 until 4 do first( i ) := last( i ) := 0;        length := 0;        sv     := n;        if sv > 0 then begin            while begin                length := length + 1;                if showFirstAndLast then begin                    if length <= 4 then first( length ) := sv;                    for lPos := 1 until 3 do last( lPos ) := last( lPos + 1 );                    last( 4 ) := sv                    end                else if sv <= upbHs and hs( sv ) not = 0 then begin                    % have a known value                                 %                    length := ( length + hs( sv ) ) - 1;                    sv     := 1                end ;                sv not = 1            end do begin                sv := if odd( sv ) then ( 3 * sv ) + 1 else sv div 2            end while_sv_ne_1 ;            if n < upbHs then hs( n ) := length        end if_sv_gt_0    end hailstone ;    begin        % test the hailstone procedure                                       %        integer HS_CACHE_SIZE;        HS_CACHE_SIZE := 100000;        begin            integer array first, last ( 1 :: 4 );            integer       length, maxLength, maxNumber;            integer array hs          ( 1 :: HS_CACHE_SIZE );            for i := 1 until HS_CACHE_SIZE do hs( i ) := 0;            hailstone( 27, first, last, length, hs, HS_CACHE_SIZE, true );            write( i_w := 1, s_w := 0                 , "27: length ", length, ", first: ["                 , first( 1 ), " ", first( 2 ), " ", first( 3 ), " ", first( 4 )                 , "] last: ["                 , last( 1 ), " ", last( 2 ), " ", last( 3 ), " ", last( 4 )                 , "]"                 );            maxNumber := 0;            maxLength := 0;            for n := 1 until 100000 do begin                hailstone( n, first, last, length, hs, HS_CACHE_SIZE, false );                if length > maxLength then begin                    maxNumber := n;                    maxLength := length                end if_length_gt_maxLength            end for_n ;            write( i_w := 1, s_w := 1, "Maximum sequence length: ", maxLength, " for: ", maxNumber )        end    endend.
Output:
27: length 112, first: [27 82 41 124] last: [8 4 2 1]
Maximum sequence length: 351  for: 77031


## APL

Works with: Dyalog APL
seq←hailstone n;next⍝ Returns the hailstone sequence for a given number seq←n                   ⍝ Init the sequence:While n≠1    next←(n÷2) (1+3×n)  ⍝ Compute both possibilities    n←next[1+2|n]       ⍝ Pick the appropriate next step    seq,←n              ⍝ Append that to the sequence:EndWhile
Output:
 5↑hailstone 2727 82 41 124 62 ¯5↑hailstone 2716 8 4 2 1 ⍴hailstone 27112 1↑{⍵[⍒↑(⍴∘hailstone)¨⍵]}⍳10000077031

## AutoHotkey

; Submitted by MasterFocus --- http://tiny.cc/iTunis ; [1] Generate the Hailstone Seq. for a number List := varNum := 7 ; starting number is 7, not counting elementsWhile ( varNum > 1 )  List .= ", " ( varNum := ( Mod(varNum,2) ? (varNum*3)+1 : varNum//2 ) )MsgBox % List ; [2] Seq. for starting number 27 has 112 elements Count := 1, List := varNum := 27 ; starting number is 27, counting elementsWhile ( varNum > 1 )  Count++ , List .= ", " ( varNum := ( Mod(varNum,2) ? (varNum*3)+1 : varNum//2 ) )MsgBox % "Sequence:n" List "nnCount: " Count ; [3] Find number<100000 with longest seq. and show both values MaxNum := Max := 0 ; reset the Maximum variablesTimesToLoop := 100000 ; limit number here is 100000Offset := 70000 ; offset - use 0 to process from 0 to 100000Loop, %TimesToLoop%{  If ( TimesToLoop < ( varNum := Index := A_Index+Offset ) )    Break  text := "Processing...n-------------------n"  text .= "Current starting number: " Index "n"  text .= "Current sequence count: " Count  text .= "n-------------------n"  text .= "Maximum starting number: " MaxNum "n"  text .= "Maximum sequence count: " Max " <<" ; text split to avoid long code lines  ToolTip, %text%  Count := 1 ; going to count the elements, but no "List" required  While ( varNum > 1 )    Count++ , varNum := ( Mod(varNum,2) ? (varNum*3)+1 : varNum//2 )  If ( Count > Max )    Max := Count , MaxNum := Index ; set the new maximum values, if necessary}ToolTipMsgBox % "Number: " MaxNum "nCount: " Max

## AutoIt

 $Hail = Hailstone(27)ConsoleWrite("Sequence-Lenght: "&$Hail&@CRLF)$Big = -1$Sequenzlenght = -1For $I = 1 To 100000$Hail = Hailstone($i, False) If Number($Hail) > $Sequenzlenght Then$Sequenzlenght = Number($Hail)$Big = $i EndIfNextConsoleWrite("Longest Sequence : "&$Sequenzlenght&" from number "&$Big&@CRLF)Func Hailstone($int, $sequence = True)$Counter = 0	While True		$Counter += 1 If$sequence = True Then ConsoleWrite($int & ",") If$int = 1 Then ExitLoop		If Not Mod($int, 2) Then$int = $int / 2 Else$int = 3 * $int + 1 EndIf If Not Mod($Counter, 25) AND $sequence = True Then ConsoleWrite(@CRLF) WEnd If$sequence = True Then ConsoleWrite(@CRLF)	Return $CounterEndFunc ;==>Hailstone  Output: 27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,91,274,137,412,206,103, 310,155,466,233,700,350,175,526,263,790,395,1186,593,1780,890,445,1336,668,334,167,502,251,754,377,1132, 566,283,850,425,1276,638,319,958,479,1438,719,2158,1079,3238,1619,4858,2429,7288,3644,1822,911,2734,1367,4102,2051, 6154,3077,9232,4616,2308,1154,577,1732,866,433,1300,650,325,976,488,244,122,61,184,92,46,23,70,35,106, 53,160,80,40,20,10,5,16,8,4,2,1, Sequence-Lenght: 112 Longest Sequence : 351 from number 77031  ## AWK  #!/usr/bin/awk -ffunction hailstone(v, verbose) { n = 1; u = v; while (1) { if (verbose) printf " "u; if (u==1) return(n); n++; if (u%2 > 0 ) u = 3*u+1; else u = u/2; } } BEGIN { i = 27; printf("hailstone(%i) has %i elements\n",i,hailstone(i,1)); ix=0; m=0; for (i=1; i<100000; i++) { n = hailstone(i,0); if (m<n) { m=n; ix=i; } } printf("longest hailstone sequence is %i and has %i elements\n",ix,m);}  Output: 27 82 41 124 ....... 8 4 2 1 hailstone(27) has 112 elements longest hailstone sequence is 77031 and has 351 elements  ## BASIC ### Applesoft BASIC 10 HOME 100 N = 27110 GOSUB 400"HAILSTONE120 DEF FN L(I) = E(I + 4 * (I < 0))130IFL=112AND(S(0)=27ANDS(1)=82ANDS(2)=41ANDS(3)=124)AND(FNL(M-3)=8ANDFNL(M-2)=4ANDFNL(M-1)=2ANDFNL(M)=1)THENPRINT"THE HAILSTONE SEQUENCE FOR THE NUMBER 27 HAS 112 ELEMENTS STARTING WITH 27, 82, 41, 124 AND ENDING WITH 8, 4, 2, 1"140 PRINT150 V = PEEK(37) + 1 200 N = 1210 GOSUB 400"HAILSTONE220 MN = 1230 ML = L240 FOR I = 2 TO 99999250 N = I260 GOSUB 400"HAILSTONE270 IFL>MLTHENMN=I:ML=L:VTABV:HTAB1:PRINT "THE NUMBER " MN " HAS A HAILSTONE SEQUENCE LENGTH OF "L" WHICH IS THE LONGEST HAILSTONE SEQUENCE OF NUMBERS LESS THAN ";:Y=PEEK(37)+1:X=PEEK(36)+1280 IF Y THEN VTAB Y : HTAB X : PRINTI+1;290 NEXT I 300 END 400 M = 0410 FOR L = 1 TO 1E38420 IF L < 5 THEN S(L-1) = N430 M = (M + 1) * (M < 3)440 E(M) = N450 IF N = 1 THEN RETURN460 EVEN = INT(N/2)=N/2470 IF EVEN THEN N=N/2480 IF NOT EVEN THEN N = (3 * N) + 1490 NEXT L : STOP ### BBC BASIC  seqlen% = FNhailstone(27, TRUE) PRINT '"Sequence length = "; seqlen% maxlen% = 0 FOR number% = 2 TO 100000 seqlen% = FNhailstone(number%, FALSE) IF seqlen% > maxlen% THEN maxlen% = seqlen% maxnum% = number% ENDIF NEXT PRINT "The number with the longest hailstone sequence is " ; maxnum% PRINT "Its sequence length is " ; maxlen% END DEF FNhailstone(N%, S%) LOCAL L% IF S% THEN PRINT N%; WHILE N% <> 1 IF N% AND 1 THEN N% = 3 * N% + 1 ELSE N% DIV= 2 IF S% THEN PRINT N%; L% += 1 ENDWHILE = L% + 1 Output:  27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Sequence length = 112 The number with the longest hailstone sequence is 77031 Its sequence length is 351  ### Commodore BASIC 100 PRINT : PRINT "HAILSTONE SEQUENCE FOR N = 27:"110 N=27 : SHOW=1120 GOSUB 1000130 PRINT X"ELEMENTS"140 PRINT : PRINT "FINDING N WITH THE LONGEST HAILSTONE SEQUENCE"150 SHOW=0160 T0 = TI170 FOR N=2 TO 100000180 : GOSUB 1000190 : IF X>MAX THEN MAX=X : NMAX = N200 : REM' PRINT N,X,MAX210 NEXT230 PRINT "LONGEST HAILSTONE SEQUENCE STARTS WITH "NMAX"."240 PRINT "IT HAS"MAX"ELEMENTS"260 END1000 REM '*** HAILSTONE SEQUENCE SUBROUTINE ***1010 X = 0 : S = N1020 IF SHOW THEN PRINT S,1030 X = X+11040 IF S=1 THEN RETURN1050 IF INT(S/2)=S/2 THEN S = S/2 : GOTO 10201060 S = 3*S+11070 GOTO 1020  ### FreeBASIC ' version 17-06-2015' compile with: fbc -s console Function hailstone_fast(number As ULongInt) As ULongInt ' faster version ' only counts the sequence Dim As ULongInt count = 1 While number <> 1 If (number And 1) = 1 Then number += number Shr 1 + 1 ' 3*n+1 and n/2 in one count += 2 Else number Shr= 1 ' divide number by 2 count += 1 End If Wend Return count End Function Sub hailstone_print(number As ULongInt) ' print the number and sequence Dim As ULongInt count = 1 Print "sequence for number "; number Print Using "########"; number; 'starting number While number <> 1 If (number And 1) = 1 Then number = number * 3 + 1 ' n * 3 + 1 count += 1 Else number = number \ 2 ' n \ 2 count += 1 End If Print Using "########"; number; Wend Print : Print Print "sequence length = "; count Print Print String(79,"-") End Sub Function hailstone(number As ULongInt) As ULongInt ' normal version ' only counts the sequence Dim As ULongInt count = 1 While number <> 1 If (number And 1) = 1 Then number = number * 3 + 1 ' n * 3 + 1 count += 1 End If number = number \ 2 ' divide number by 2 count += 1 Wend Return count End Function ' ------=< MAIN >=------ Dim As ULongInt numberDim As UInteger x, max_x, max_seq hailstone_print(27)Print For x As UInteger = 1 To 100000 number = hailstone(x) If number > max_seq Then max_x = x max_seq = number End IfNext Print "The longest sequence is for "; max_x; ", it has a sequence length of "; max_seq ' empty keyboard bufferWhile Inkey <> "" : WendPrint : Print : Print "hit any key to end program"SleepEnd Output: sequence for number 27 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 sequence length = 112 ------------------------------------------------------------------------------- The longest sequence is for 77031, it has a sequence length of 351 ### Liberty BASIC print "Part 1: Create a routine to generate the hailstone sequence for a number."print ""while hailstone < 1 or hailstone <> int(hailstone) input "Please enter a positive integer: "; hailstonewendprint ""print "The following is the 'Hailstone Sequence' for your number..."print ""print hailstonewhile hailstone <> 1 if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1 print hailstonewendprint ""input "Hit 'Enter' to continue to part 2...";dummy$clsprint "Part 2: Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1."print ""print "No. in Seq.","Hailstone Sequence Number for 27"print ""c = 1: hailstone = 27print c, hailstonewhile hailstone <> 1    c = c + 1    if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1    print c, hailstonewendprint ""input "Hit 'Enter' to continue to part 3...";dummy$clsprint "Part 3: Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.(But don't show the actual sequence)!"print ""print "Calculating result... Please wait... This could take a little while..."print ""print "Percent Done", "Start Number", "Seq. Length", "Maximum Sequence So Far"print ""for cc = 1 to 99999 hailstone = cc: c = 1 while hailstone <> 1 c = c + 1 if hailstone / 2 = int(hailstone / 2) then hailstone = hailstone / 2 else hailstone = (3 * hailstone) + 1 wend if c > max then max = c: largesthailstone = cc locate 1, 7 print " " locate 1, 7 print using("###.###", cc / 99999 * 100);"%", cc, c, max scannext ccprint ""print "The number less than 100,000 with the longest 'Hailstone Sequence' is "; largesthailstone;". It's sequence length is "; max;"."end ### OxygenBasic  function Hailstone(sys *n)'=========================if n and 1 n=n*3+1else n=n>>1end ifend function function HailstoneSequence(sys n) as sys'=======================================count=1do Hailstone n Count++ if n=1 then exit doend doreturn countend function 'MAIN'==== maxc=0maxn=0e=100000for n=1 to e c=HailstoneSequence n if c>maxc maxc=c maxn=n end ifnext print e ", " maxn ", " maxc 'result 100000, 77031, 351  ### PureBasic NewList Hailstones.i() ; Make a linked list to use as we do not know the numbers of elements needed for an Array Procedure.i FillHailstones(n) ; Fills the list & returns the amount of elements in the list Shared Hailstones() ; Get access to the Hailstones-List ClearList(Hailstones()) ; Remove old data Repeat AddElement(Hailstones()) ; Add an element to the list Hailstones()=n ; Fill current value in the new list element If n=1 ProcedureReturn ListSize(Hailstones()) ElseIf n%2=0 n/2 Else n=(3*n)+1 EndIf ForEverEndProcedure If OpenConsole() Define i, l, maxl, maxi l=FillHailstones(27) Print("#27 has "+Str(l)+" elements and the sequence is: "+#CRLF$)  ForEach Hailstones()    If i=6      Print(#CRLF$) i=0 EndIf i+1 Print(RSet(Str(Hailstones()),5)) If Hailstones()<>1 Print(", ") EndIf Next i=1 Repeat l=FillHailstones(i) If l>maxl maxl=l maxi=i EndIf i+1 Until i>=100000 Print(#CRLF$+#CRLF$+"The longest sequence below 100000 is #"+Str(maxi)+", and it has "+Str(maxl)+" elements.") Print(#CRLF$+#CRLF$+"Press ENTER to exit."): Input() CloseConsole()EndIf Output:  #27 has 112 elements and the sequence is: 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 The longest sequence found up to 100000 is #77031 which has 351 elements. Press ENTER to exit.  ### Run BASIC print "Part 1: Create a routine to generate the hailstone sequence for a number."print "" while hailstone < 1 or hailstone <> int(hailstone) input "Please enter a positive integer: "; hailstonewendcount = doHailstone(hailstone,"Y") print: print "Part 2: Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1."count = doHailstone(27,"Y") print: print "Part 3: Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length.(But don't show the actual sequence)!"print "Calculating result... Please wait... This could take a little while..."print "Stone Percent Count"for i = 1 to 99999 count = doHailstone(i,"N") if count > maxCount then theBigStone = i maxCount = count print using("#####",i);" ";using("###.#", i / 99999 * 100);"% ";using("####",count) end ifnext iend '---------------------------------------------' pass number and print (Y/N)FUNCTION doHailstone(hailstone,prnt$)if prnt$= "Y" then print print "The following is the 'Hailstone Sequence' for number:";hailstoneend ifwhile hailstone <> 1 if (hailstone and 1) then hailstone = (hailstone * 3) + 1 else hailstone = hailstone / 2 doHailstone = doHailstone + 1 if prnt$ = "Y" then     print hailstone;chr$(9); if (doHailstone mod 10) = 0 then print end ifwendEND FUNCTION ## Batch File 1. Create a routine to generate the hailstone sequence for a number. 2. Show that the hailstone sequence for the number 27 has 112 elements... @echo offsetlocal enabledelayedexpansionecho.::Task #1call :hailstone 111echo Task #1: (Start:!sav!)echo !seq!echo.echo Sequence has !cnt! elements.echo.::Task #2call :hailstone 27echo Task #2: (Start:!sav!)echo !seq!echo.echo Sequence has !cnt! elements.echo.pause>nulexit /b 0::The Function:hailstoneset num=%1set seq=%1set sav=%1set cnt=0 :loopset /a cnt+=1if !num! equ 1 goto :eofset /a isodd=%num%%%2if !isodd! equ 0 goto divideby2 set /a num=(3*%num%)+1set seq=!seq! %num%goto loop :divideby2set /a num/=2set seq=!seq! %num%goto loop Output: Task #1: (Start:111) 111 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Sequence has 70 elements. Task #2: (Start:27) 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Sequence has 112 elements. The script above could only be used in smaller inputs. Thus, for the third task, a slightly different script will be used. However, this script is still slow. I tried this on a fast computer and it took about 40-45 minutes to complete. @echo offsetlocal enableDelayedExpansionif "%~1"=="test" ( for /l %%. in () do ( set /a "test1=num %% 2, cnt=cnt+1" if !test1! equ 0 (set /a num/=2 & if !num! equ 1 exit !cnt!) else (set /a num=3*num+1) )) set max=0set record=0 for /l %%X in (2,1,100000) do ( set num=%%X & cmd /c "%~f0" test if !errorlevel! gtr !max! (set /a "max=!errorlevel!,record=%%X"))set /a max+=1 echo.Number less than 100000 with longest sequence: %record%echo.With length %max%.pause>nul exit /b 0 Output: Number less than 100000 with longest sequence: 77031 With length 351. ## beeswax This approach reuses the main hailstone sequence function for all three tasks. The pure hailstone sequence function, returning the sequence for any number entered in the console:  >@:N q>%"[email protected]d~2~pL~1F{<T_ Returning the sequence for the starting value 27  >@:N q>%"[email protected]d~2~qL~1Ff{<BF3_{NNgA< Output of the sequence, followed by the length of the sequence:  27824112462319447 ... 215810793238161948582429728836441822 ... 168421 112 Number below 100,000 with the longest hailstone sequence, and the length of that sequence:  >@: q pf1_#>%"[email protected]#{g? {[email protected][email protected]@q'M<d~2~pL~1Ff< < >?d >[email protected][email protected][email protected]~3~hAg?M d >[email protected]?Mb Output: 77031 351 ## Befunge 93*:. v > :2%v >v+1*3_2/>" ",:.v v<<v v-1:< <+1\_$1+v^ \  v .,+94<>^>::v>" "03pv  :* pv67:" "<  0: 1>p78p25  *^*p0  v!-1:  <<*^<9$_:0\ ^-^< vv01g00:< 1 4>g"@"*+v^ <+v01/"@":_$ ^,>p"@"%00p\$:^.vg01g00 ,+49<>"@"*[email protected]  Output: 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 112 77031 351 ## Bracmat ( ( hailstone = L len . !arg:?L & whl ' ( !arg:~1 & (!arg*1/2:~/|3*!arg+1):?arg & !arg !L:?L ) & (!L:? [?len&!len.!L) )& ( reverse = L e . :?L & whl'(!arg:%?e ?arg&!e !L:?L) & !L )& hailstone$27:(?len.?list)& reverse$!list:?first4 [4 ? [-5 ?last4& put$"Hailstone sequence starting with "& put$!first4& put$(str$(" has " !len " elements and ends with "))& put$(!last4 \n)& 1:?N& 0:?max:?Nmax&   whl  ' ( !N+1:<100000:?N    &   hailstone$!N : ( >!max:?max&!N:?Nmax | ? . ? ) )& out$ ( str    $( "The number <100000 with the longest hailstone sequence is " !Nmax " with " !max " elements." ) )); ## Brainf***  This example is incomplete. Please ensure that it meets all task requirements and remove this message. Prints the number of terms required to map the input to 1. Does not count the first term of the sequence. >,[ [ ----------[ >>>[>>>>]+[[-]+<[->>>>++>>>>+[>>>>]++[->+<<<<<]]<<<] ++++++[>------<-]>--[>>[->>>>]+>+[<<<<]>-],< ]> ]>>>++>+>>[ <<[>>>>[-]+++++++++<[>-<-]+++++++++>[-[<->-]+[<<<<]]<[>+<-]>] >[>[>>>>]+[[-]<[+[->>>>]>+<]>[<+>[<<<<]]+<<<<]>>>[->>>>]+>+[<<<<]] >[[>+>>[<<<<+>>>>-]>]<<<<[-]>[-<<<<]]>>>>>>> ]>>+[[-]++++++>>>>]<<<<[[<++++++++>-]<.[-]<[-]<[-]<]<,] 27111 ## Brat hailstone = { num | sequence = [num] while { num != 1 } { true? num % 2 == 0 { num = num / 2 } { num = num * 3 + 1 } sequence << num } sequence} #Check sequence for 27seq = hailstone 27true? (seq[0,3] == [27 82 41 124] && seq[-1, -4] == [8 4 2 1]) { p "Sequence for 27 is correct" } { p "Sequence for 27 is not correct!" } #Find longest sequence for numbers < 100,000longest = [number: 0 length: 0] 1.to 99999 { index | seq = hailstone index true? seq.length > longest[:length] { longest[:length] = seq.length longest[:number] = index p "Longest so far: #{index} @ #{longest[:length]} elements" } index = index + 1 } p "Longest was starting from #{longest[:number]} and was of length #{longest[:length]}" Output: Sequence for 27 is correct Longest so far: 1 @ 1 elements Longest so far: 2 @ 2 elements Longest so far: 3 @ 8 elements ... Longest so far: 52527 @ 340 elements Longest so far: 77031 @ 351 elements Longest was starting from 77031 and was of length 351 ## Burlesque  blsq ) 27{^^^^2.%{3.*1.+}\/{2./}\/ie}{1!=}w!bx{\/+]}{\/isn!}w!L[112  ## C #include <stdio.h>#include <stdlib.h> int hailstone(int n, int *arry){ int hs = 1; while (n!=1) { hs++; if (arry) *arry++ = n; n = (n&1) ? (3*n+1) : (n/2); } if (arry) *arry++ = n; return hs;} int main(){ int j, hmax = 0; int jatmax, n; int *arry; for (j=1; j<100000; j++) { n = hailstone(j, NULL); if (hmax < n) { hmax = n; jatmax = j; } } n = hailstone(27, NULL); arry = malloc(n*sizeof(int)); n = hailstone(27, arry); printf("[ %d, %d, %d, %d, ...., %d, %d, %d, %d] len=%d\n", arry[0],arry[1],arry[2],arry[3], arry[n-4], arry[n-3], arry[n-2], arry[n-1], n); printf("Max %d at j= %d\n", hmax, jatmax); free(arry); return 0;} Output: [ 27, 82, 41, 124, ...., 8, 4, 2, 1] len= 112 Max 351 at j= 77031 ### With caching Much faster if you want to go over a million or so. #include <stdio.h> #define N 10000000#define CS N /* cache size */ typedef unsigned long ulong;ulong cache[CS] = {0}; ulong hailstone(ulong n){ int x; if (n == 1) return 1; if (n < CS && cache[n]) return cache[n]; x = 1 + hailstone((n & 1) ? 3 * n + 1 : n / 2); if (n < CS) cache[n] = x; return x;} int main(){ int i, l, max = 0, mi; for (i = 1; i < N; i++) { if ((l = hailstone(i)) > max) { max = l; mi = i; } } printf("max below %d: %d, length %d\n", N, mi, max); return 0;} ## C# using System;using System.Collections.Generic;using System.Linq;using System.Text; namespace Hailstone{ class Program { public static List<int> hs(int n,List<int> seq) { List<int> sequence = seq; sequence.Add(n); if (n == 1) { return sequence; }else{ int newn = (n % 2 == 0) ? n / 2 : (3 * n) + 1; return hs(newn, sequence); } } static void Main(string[] args) { int n = 27; List<int> sequence = hs(n,new List<int>()); Console.WriteLine(sequence.Count + " Elements"); List<int> start = sequence.GetRange(0, 4); List<int> end = sequence.GetRange(sequence.Count - 4, 4); Console.WriteLine("Starting with : " + string.Join(",", start) + " and ending with : " + string.Join(",", end)); int number = 0, longest = 0; for (int i = 1; i < 100000; i++) { int count = (hs(i, new List<int>())).Count; if (count > longest) { longest = count; number = i; } } Console.WriteLine("Number < 100000 with longest Hailstone seq.: " + number + " with length of " + longest); } }} 112 Elements Starting with : 27,82,41,124 and ending with : 8,4,2,1 Number < 100000 with longest Hailstone seq.: 77031 with length of 351  ### With caching As with the C example, much faster if you want to go over a million or so. using System;using System.Collections.Generic; namespace ConsoleApplication1{ class Program { public static void Main() { int longestChain = 0, longestNumber = 0; var recursiveLengths = new Dictionary<int, int>(); const int maxNumber = 100000; for (var i = 1; i <= maxNumber; i++) { var chainLength = Hailstone(i, recursiveLengths); if (longestChain >= chainLength) continue; longestChain = chainLength; longestNumber = i; } Console.WriteLine("max below {0}: {1} ({2} steps)", maxNumber, longestNumber, longestChain); } private static int Hailstone(int num, Dictionary<int, int> lengths) { if (num == 1) return 1; while (true) { if (lengths.ContainsKey(num)) return lengths[num]; lengths[num] = 1 + ((num%2 == 0) ? Hailstone(num/2, lengths) : Hailstone((3*num) + 1, lengths)); } } }} max below 100000: 77031 (351 steps)  ## C++ #include <iostream>#include <vector>#include <utility> std::vector<int> hailstone(int i){ std::vector<int> v; while(true){ v.push_back(i); if (1 == i) break; i = (i % 2) ? (3 * i + 1) : (i / 2); } return v;} std::pair<int,int> find_longest_hailstone_seq(int n){ std::pair<int, int> maxseq(0, 0); int l; for(int i = 1; i < n; ++i){ l = hailstone(i).size(); if (l > maxseq.second) maxseq = std::make_pair(i, l); } return maxseq;} int main () { // Use the routine to show that the hailstone sequence for the number 27 std::vector<int> h27; h27 = hailstone(27); // has 112 elements int l = h27.size(); std::cout << "length of hailstone(27) is " << l;// starting with 27, 82, 41, 124 and std::cout << " first four elements of hailstone(27) are "; std::cout << h27[0] << " " << h27[1] << " " << h27[2] << " " << h27[3] << std::endl;// ending with 8, 4, 2, 1 std::cout << " last four elements of hailstone(27) are " << h27[l-4] << " " << h27[l-3] << " " << h27[l-2] << " " << h27[l-1] << std::endl; std::pair<int,int> m = find_longest_hailstone_seq(100000); std::cout << "the longest hailstone sequence under 100,000 is " << m.first << " with " << m.second << " elements." <<std::endl; return 0;} Output:  length of hailstone(27) is 112 first four elements of hailstone(27) are 27 82 41 124 last four elements of hailstone(27) are 8 4 2 1 the longest hailstone sequence under 100,000 is 77031 with 351 elements.  ## Ceylon shared void run() { {Integer*} hailstone(variable Integer n) { variable [Integer*] stones = [n]; while(n != 1) { n = if(n.even) then n / 2 else 3 * n + 1; stones = stones.append([n]); } return stones; } value hs27 = hailstone(27); print("hailstone sequence for 27 is hs27.take(3)...hs27.skip(hs27.size - 3).take(3) with length hs27.size"); variable value longest = hailstone(1); for(i in 2..100k - 1) { value current = hailstone(i); if(current.size > longest.size) { longest = current; } } print("the longest sequence under 100,000 starts with longest.first else "what?" and has length longest.size");} ## CLIPS (deftemplate longest (slot bound) ; upper bound for the range of values to check (slot next (default 2)) ; next value that needs to be checked (slot start (default 1)) ; starting value of longest sequence (slot len (default 1)) ; length of longest sequence) (deffacts startup (query 27) (longest (bound 100000))) (deffunction hailstone-next (?n) (if (evenp ?n) then (div ?n 2) else (+ (* 3 ?n) 1) )) (defrule extend-sequence ?hail <- (hailstone$?sequence ?tail&:(> ?tail 1))  =>  (retract ?hail)  (assert (hailstone ?sequence ?tail (hailstone-next ?tail)))) (defrule start-query  (query ?num)  =>  (assert (hailstone ?num))) (defrule result-query  (query ?num)  (hailstone ?num $?sequence 1) => (bind ?sequence (create$ ?num ?sequence 1))  (printout t "Hailstone sequence starting with " ?num ":" crlf)  (bind ?len (length ?sequence))  (printout t "  Length: " ?len crlf)  (printout t "  First four: " (implode$(subseq$ ?sequence 1 4)) crlf)  (printout t "  Last four: " (implode$(subseq$ ?sequence (- ?len 3) ?len)) crlf)  (printout t crlf)) (defrule longest-create-next-hailstone  (longest (bound ?bound) (next ?next))  (test (<= ?next ?bound))  (not (hailstone ?next $?)) => (assert (hailstone ?next))) (defrule longest-check-next-hailstone ?longest <- (longest (bound ?bound) (next ?next) (start ?start) (len ?len)) (test (<= ?next ?bound)) ?hailstone <- (hailstone ?next$?sequence 1)  =>  (retract ?hailstone)  (bind ?thislen (+ 2 (length ?sequence)))  (if (> ?thislen ?len) then    (modify ?longest (start ?next) (len ?thislen) (next (+ ?next 1)))    else    (modify ?longest (next (+ ?next 1)))  )) (defrule longest-finished  (longest (bound ?bound) (next ?next) (start ?start) (len ?len))  (test (> ?next ?bound))  =>  (printout t "The number less than " ?bound " that has the largest hailstone" crlf)  (printout t "sequence is " ?start " with a length of " ?len "." crlf)  (printout t crlf))
Output:
The number less than 100000 that has the largest hailstone
sequence is 77031 with a length of 351.

Hailstone sequence starting with 27:
Length: 112
First four: 27 82 41 124
Last four: 8 4 2 1

## Clojure

(defn hailstone-seq [n]  {:pre [(pos? n)]}  (lazy-seq    (cond (= n 1)   '(1)         (even? n) (cons n (hailstone-seq (/ n 2)))         :else     (cons n (hailstone-seq (+ (* n 3) 1)))))) (let [hseq (hailstone-seq 27)]  (->  hseq count      (= 112)            assert)  (->> hseq (take 4)   (= [27 82 41 124]) assert)  (->> hseq (drop 108) (= [8 4 2 1])      assert)) (let [{max-i :num, max-len :len}      (reduce #(max-key :len %1 %2)              (for [i (range 1 100000)]                {:num i, :len (count (hailstone-seq i))}))]  (println "Maximum length" max-len "was found for hailstone(" max-i ")."))

## COBOL

Testing with GnuCOBOL

       identification division.       program-id. hailstones.       remarks. cobc -x hailstones.cob.        data division.       working-storage section.       01 most                 constant as 1000000.       01 coverage             constant as 100000.              01 stones               usage binary-long.       01 n                    usage binary-long.       01 storm                usage binary-long.        01 show-arg             pic 9(6).       01 show-default         pic 99 value 27.       01 show-sequence        usage binary-long.       01 longest              usage binary-long occurs 2 times.        01 filler.          05 hail              usage binary-long                               occurs 0 to most depending on stones.       01 show                 pic z(10).       01 low-range            usage binary-long.       01 high-range           usage binary-long.       01 range                usage binary-long.         01 remain               usage binary-long.       01 unused               usage binary-long.        procedure division.       accept show-arg from command-line       if show-arg less than 1 or greater than coverage then           move show-default to show-arg       end-if       move show-arg to show-sequence        move 1 to longest(1)       perform hailstone varying storm                         from 1 by 1 until storm > coverage       display "Longest at: " longest(2) " with " longest(1) " elements"       goback.       *> **************************************************************       hailstone.       move 0 to stones       move storm to n       perform until n equal 1           if stones > most then               display "too many hailstones" upon syserr               stop run           end-if            add 1 to stones           move n to hail(stones)           divide n by 2 giving unused remainder remain           if remain equal 0 then               divide 2 into n           else               compute n = 3 * n + 1           end-if       end-perform       add 1 to stones       move n to hail(stones)        if stones > longest(1) then           move stones to longest(1)           move storm to longest(2)       end-if        if storm equal show-sequence then           display show-sequence ": " with no advancing           perform varying range from 1 by 1 until range > stones               move 5 to low-range               compute high-range = stones - 4               if range < low-range or range > high-range then                   move hail(range) to show                   display function trim(show) with no advancing                   if range < stones then                       display ", " with no advancing                   end-if               end-if               if range = low-range and stones > 8 then                   display "..., " with no advancing               end-if           end-perform           display ": " stones " elements"       end-if       .        end program hailstones.
Output:
prompt$cobc -x hailstones.cob prompt$ ./hailstones
+0000000027: 27, 82, 41, 124, ..., 8, 4, 2, 1: +0000000112 elements
Longest at: +0000077031 with +0000000351 elements
prompt$./hailstones 42 +0000000042: 42, 21, 64, 32, ..., 8, 4, 2, 1: +0000000009 elements Longest at: +0000077031 with +0000000351 elements  ## CoffeeScript Recursive version: hailstone = (n) -> if n is 1 [n] else if n % 2 is 0 [n].concat hailstone n/2 else [n].concat hailstone (3*n) + 1 h27 = hailstone 27console.log "hailstone(27) = #{h27[0..3]} ... #{h27[-4..]} (length: #{h27.length})" maxlength = 0maxnums = [] for i in [1..100000] seq = hailstone i if seq.length is maxlength maxnums.push i else if seq.length > maxlength maxlength = seq.length maxnums = [i] console.log "Max length: #{maxlength}; numbers generating sequences of this length: #{maxnums}" hailstone(27) = 27,82,41,124 ... 8,4,2,1 (length: 112) Max length: 351; numbers generating sequences of this length: 77031 ## Common Lisp (defun hailstone (n) (cond ((= n 1) '(1)) ((evenp n) (cons n (hailstone (/ n 2)))) (t (cons n (hailstone (+ (* 3 n) 1)))))) (defun longest (n) (let ((k 0) (l 0)) (loop for i from 1 below n do (let ((len (length (hailstone i)))) (when (> len l) (setq l len k i))) finally (format t "Longest hailstone sequence under ~A for ~A, having length ~A." n k l)))) Sample session: ROSETTA> (length (hailstone 27)) 112 ROSETTA> (subseq (hailstone 27) 0 4) (27 82 41 124) ROSETTA> (last (hailstone 27) 4) (8 4 2 1) ROSETTA> (longest-hailstone 100000) Longest hailstone sequence under 100000 for 77031, having length 351. NIL ## Crystal  def hailstone(n) seq = [n] until n == 1 n = n.even? ? n / 2 : n * 3 + 1 seq << n end seqend max_len = (1...100_000).max_by{|n| hailstone(n).size }max = hailstone(max_len)puts ([max_len, max.size, max.max, max.first(4), max.last(4)])# => [77031, 351, 21933016, [77031, 231094, 115547, 346642], [8, 4, 2, 1]] twenty_seven = hailstone(27)puts ([twenty_seven.size, twenty_seven.first(4), max.last(4)])# => [112, [27, 82, 41, 124], [8, 4, 2, 1]]  ## D ### Basic Version import std.stdio, std.algorithm, std.range, std.typecons; auto hailstone(uint n) pure nothrow { auto result = [n]; while (n != 1) { n = (n & 1) ? (n * 3 + 1) : (n / 2); result ~= n; } return result;} void main() { enum M = 27; immutable h = M.hailstone; writeln("hailstone(", M, ")= ", h[0 .. 4], " ... " , h[$ - 4 .. $]); writeln("Length hailstone(", M, ")= ", h.length); enum N = 100_000; immutable p = iota(1, N) .map!(i => tuple(i.hailstone.length, i)) .reduce!max; writeln("Longest sequence in [1,", N, "]= ",p[1]," with len ",p[0]);} Output: hailstone(27)= [27, 82, 41, 124] ... [8, 4, 2, 1] Length hailstone(27)= 112 Longest sequence in [1,100000]= 77031 with len 351 ### Lazy Version Same output. import std.stdio, std.algorithm, std.typecons, std.range; auto hailstone(uint m) pure nothrow @nogc { return m .recurrence!q{ a[n - 1] & 1 ? a[n - 1] * 3 + 1 : a[n - 1]/2} .until!q{ a == 1 }(OpenRight.no);} void main() { enum M = 27; immutable h = M.hailstone.array; writeln("hailstone(", M, ")= ", h[0 .. 4], " ... " , h[$ - 4 .. $]); writeln("Length hailstone(", M, ")= ", h.length); enum N = 100_000; immutable p = iota(1, N) .map!(i => tuple(i.hailstone.walkLength, i)) .reduce!max; writeln("Longest sequence in [1,", N, "]= ",p[1]," with len ",p[0]);} ### Faster Lazy Version Same output. struct Hailstone { uint n; bool empty() const pure nothrow @nogc { return n == 0; } uint front() const pure nothrow @nogc { return n; } void popFront() pure nothrow @nogc { n = n == 1 ? 0 : (n & 1 ? (n * 3 + 1) : n / 2); }} void main() { import std.stdio, std.algorithm, std.range, std.typecons; enum M = 27; immutable h = M.Hailstone.array; writeln("hailstone(", M, ")= ", h[0 .. 4], " ... " , h[$ - 4 .. $]); writeln("Length hailstone(", M, ")= ", h.length); enum N = 100_000; immutable p = iota(1, N) .map!(i => tuple(i.Hailstone.walkLength, i)) .reduce!max; writeln("Longest sequence in [1,", N, "]= ",p[1]," with len ",p[0]);} ### Lazy Version With Caching Faster, same output. import std.stdio, std.algorithm, std.range, std.typecons; struct Hailstone(size_t cacheSize = 500_000) { size_t n; __gshared static size_t[cacheSize] cache; bool empty() const pure nothrow @nogc { return n == 0; } size_t front() const pure nothrow @nogc { return n; } void popFront() nothrow { if (n >= cacheSize) { n = n == 1 ? 0 : (n & 1 ? n*3 + 1 : n/2); } else if (cache[n]) { n = cache[n]; } else { immutable n2 = n == 1 ? 0 : (n & 1 ? n*3 + 1 : n/2); n = cache[n] = n2; } }} void main() { enum M = 27; const h = M.Hailstone!().array; writeln("hailstone(", M, ")= ", h[0 .. 4], " ... " , h[$ - 4 .. $]); writeln("Length hailstone(", M, ")= ", h.length); enum N = 100_000; immutable p = iota(1, N) .map!(i => tuple(i.Hailstone!().walkLength, i)) .reduce!max; writeln("Longest sequence in [1,", N, "]= ",p[1]," with len ",p[0]);} ### Generator Range Version import std.stdio, std.algorithm, std.range, std.typecons, std.concurrency; auto hailstone(size_t n) { return new Generator!size_t({ yield(n); while (n > 1) { n = (n & 1) ? (3 * n + 1) : (n / 2); yield(n); } });} void main() { enum M = 27; const h = M.hailstone.array; writeln("hailstone(", M, ")= ", h[0 .. 4], " ... " , h[$ - 4 .. $]); writeln("Length hailstone(", M, ")= ", h.length); enum N = 100_000; immutable p = iota(1, N) .map!(i => tuple(i.hailstone.walkLength, i)) .reduce!max; writeln("Longest sequence in [1,", N, "]= ",p[1]," with len ",p[0]);} ## Dart List<int> hailstone(int n) { if(n<=0) { throw new IllegalArgumentException("start value must be >=1)"); } Queue<int> seq=new Queue<int>(); seq.add(n); while(n!=1) { n=n%2==0?(n/2).toInt():3*n+1; seq.add(n); } return new List<int>.from(seq);} // apparently List is missing toString()String iterableToString(Iterable seq) { String str="["; Iterator i=seq.iterator(); while(i.hasNext()) { str+=i.next(); if(i.hasNext()) { str+=","; } } return str+"]";} main() { for(int i=1;i<=10;i++) { print("h($i)="+iterableToString(hailstone(i)));  }  List<int> h27=hailstone(27);  List<int> first4=h27.getRange(0,4);  print("first 4 elements of h(27): "+iterableToString(first4));  Expect.listEquals([27,82,41,124],first4);   List<int> last4=h27.getRange(h27.length-4,4);  print("last 4 elements of h(27): "+iterableToString(last4));  Expect.listEquals([8,4,2,1],last4);   print("length of sequence h(27): "+h27.length);  Expect.equals(112,h27.length);   int seq,max=0;  for(int i=1;i<=100000;i++) {    List<int> h=hailstone(i);    if(h.length>max) {      max=h.length;      seq=i;    }  }  print("up to 100000 the sequence h($seq) has the largest length ($max)");}
Output:
h(1)=[1]
h(2)=[2,1]
h(3)=[3,10,5,16,8,4,2,1]
h(4)=[4,2,1]
h(5)=[5,16,8,4,2,1]
h(6)=[6,3,10,5,16,8,4,2,1]
h(7)=[7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1]
h(8)=[8,4,2,1]
h(9)=[9,28,14,7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1]
h(10)=[10,5,16,8,4,2,1]
first 4 elements of h(27): [27,82,41,124]
last 4 elements of h(27): [8,4,2,1]
length of sequence h(27): 112
up to 100000 the sequence h(77031) has the largest length (351)

## Dc

Firstly, this code takes the value from the stack, computes and prints the corresponding Hailstone sequence, and the length of the sequence. The q procedure is for counting the length of the sequence. The e and o procedure is for even and odd number respectively. The x procedure is for overall control.

27[[--: ]nzpq]sq[d 2/ p]se[d 3*1+ p]so[d2% 0=e d1=q d2% 1=o d1=q lxx]dsxx
Output:
82
41
124
62
(omitted)
8
4
2
1
--: 112


Then we could wrap the procedure x with a new procedure s, and call it with l which is loops the value of t from 1 to 100000, and cleaning up the stack after each time we finish up with a number. Register L for the length of the longest sequence and T for the corresponding number. Also, procedure q is slightly modified for storing L and T if needed, and all printouts in procedure e and o are muted.

0dsLsT1st[dsLltsT]sM[[zdlL<M q]sq[d 2/]se[d 3*1+ ]so[d2% 0=e d1=q d2% 1=o d1=q lxx]dsxx]ss[lt1+dstlsxc lt100000>l]dslxlTn[:]nlLp 
Output:
(Takes quite some time on a decent machine)
77031:351

## DCL

$n = f$integer( p1 )$i = 1$ loop:$if p2 .nes. "QUIET" then$ s'i = n$if n .eq. 1 then$ goto done$i = i + 1$  if .not. n$then$   n = n / 2$else$   if n .gt. 715827882 then $exit ! avoid overflowing$   n = 3 * n + 1$endif$  goto loop$done:$ if p2 .nes. "QUIET"$then$  penultimate_i = i - 1$antepenultimate_i = i - 2$  preantepenultimate_i = i - 3$write sys$output "sequence has ", i, " elements starting with ", s1, ", ", s2, ", ", s3, ", ", s4, " and ending with ", s'preantepenultimate_i, ", ", s'antepenultimate_i, ", ", s'penultimate_i, ", ", s'i$endif$ sequence_length == i
Output:
$@hailstone 27 sequence has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1 $ limit = f$integer( p1 )$ i = 1$max_so_far = 0$ loop:$call hailstone 'i quiet$  if sequence_length .gt. max_so_far$then$   max_so_far = sequence_length$current_record_holder = i$  endif$i = i + 1$  if i .lt. limit then $goto loop$ write sys$output current_record_holder, " is the number less than ", limit, " which has the longest hailstone sequence which is ", max_so_far, " in length"$ exit$$hailstone: subroutine n = finteger( p1 ) i = 1 loop: if p2 .nes. "QUIET" then  s'i = n if n .eq. 1 then  goto done i = i + 1 if .not. n then n = n / 2 else if n .gt. 715827882 then  exit ! avoid overflowing n = 3 * n + 1 endif goto loop done: if p2 .nes. "QUIET" then penultimate_i = i - 1 antepenultimate_i = i - 2 preantepenultimate_i = i - 3 write sysoutput "sequence has ", i, " elements starting with ", s1, ", ", s2, ", ", s3, ", ", s4, " and ending with ", s'preantepenultimate_i, ", ", s'antepenultimate_i, ", ", s'penultimate_i, ", ", s'i endif sequence_length == I exit endsubroutine Output:  @longest_hailstone 100000 77031 is the number less than 100000 which has the longest hailstone sequence which is 351 in length ## Déjà Vu local hailstone: swap [ over ] while < 1 dup: if % over 2: #odd ++ * 3 else: #even / swap 2 swap push-through rot dup drop if = (name) :(main): local :h27 hailstone 27 !. = 112 len h27 !. = 27 h27! 0 !. = 82 h27! 1 !. = 41 h27! 2 !. = 124 h27! 3 !. = 8 h27! 108 !. = 4 h27! 109 !. = 2 h27! 110 !. = 1 h27! 111 local :max 0 local :maxlen 0 for i range 1 99999: dup len hailstone i if < maxlen: set :maxlen set :max i else: drop !print( "number: " to-str max ", length: " to-str maxlen )else: @hailstone Output: true true true true true true true true true number: 77031, length: 351 ## Delphi program ShowHailstoneSequence; {APPTYPE CONSOLE} uses SysUtils, Generics.Collections; procedure GetHailstoneSequence(aStartingNumber: Integer; aHailstoneList: TList<Integer>);var n: Integer;begin aHailstoneList.Clear; aHailstoneList.Add(aStartingNumber); n := aStartingNumber; while n <> 1 do begin if Odd(n) then n := (3 * n) + 1 else n := n div 2; aHailstoneList.Add(n); end;end; var i: Integer; lList: TList<Integer>; lMaxSequence: Integer; lMaxLength: Integer;begin lList := TList<Integer>.Create; try GetHailstoneSequence(27, lList); Writeln(Format('27: %d elements', [lList.Count])); Writeln(Format('[%d,%d,%d,%d ... %d,%d,%d,%d]', [lList[0], lList[1], lList[2], lList[3], lList[lList.Count - 4], lList[lList.Count - 3], lList[lList.Count - 2], lList[lList.Count - 1]])); Writeln; lMaxSequence := 0; lMaxLength := 0; for i := 1 to 100000 do begin GetHailstoneSequence(i, lList); if lList.Count > lMaxLength then begin lMaxSequence := i; lMaxLength := lList.Count; end; end; Writeln(Format('Longest sequence under 100,000: %d with %d elements', [lMaxSequence, lMaxLength])); finally lList.Free; end; Readln;end. Output: 27: 112 elements [27 82 41 124 ... 8 4 2 1] Longest sequence under 100,000: 77031 with 351 elements ## EchoLisp  (lib 'hash)(lib 'sequences)(lib 'compile) (define (hailstone n)(when (> n 1) (if (even? n) (/ n 2) (1+ (* n 3))))) (define H (make-hash)) ;; (iterator/f seed f) returns seed, (f seed) (f(f seed)) ... (define (hlength seed) (define collatz (iterator/f hailstone seed)) (or (hash-ref H seed) ;; known ? (hash-set H seed (for ((i (in-naturals)) (h collatz)) ;; add length of subsequence if already known #:break (hash-ref H h) => (+ i (hash-ref H h)) (1+ i))))) (define (task (nmax 100000)) (for ((n [1 .. nmax])) (hlength n)) ;; fill hash table (define hmaxlength (apply max (hash-values H))) (define hmaxseed (hash-get-key H hmaxlength)) (writeln 'maxlength= hmaxlength 'for hmaxseed))  Output:  (define H27 (iterator/f hailstone 27))(take H27 6) → (27 82 41 124 62 31)(length H27) → 112(list-tail (take H27 112) -6) → (5 16 8 4 2 1) (task)maxlength= 351 for 77031 ;; more ...(lib 'bigint) (task 200000) maxlength= 383 for 156159 (task 300000) maxlength= 443 for 230631 (task 400000) maxlength= 443 for 230631 (task 500000) maxlength= 449 for 410011 (task 600000) maxlength= 470 for 511935 (task 700000) maxlength= 509 for 626331 (task 800000) maxlength= 509 for 626331 (task 900000) maxlength= 525 for 837799 (task 1000000) maxlength= 525 for 837799  ## Egel  import "prelude.eg" namespace Hailstone ( using System using List def even = [ N -> (N%2) == 0 ] def hailstone = [ 1 -> {1} | N -> if even N then cons N (hailstone (N/2)) else cons N (hailstone (N * 3 + 1)) ] def hailpair = [ N -> (N, length (hailstone N)) ] def hailmax = [ (N, NMAX), (M, MMAX) -> if (NMAX < MMAX) then (M, MMAX) else (N, NMAX) ] def largest = [ 1 -> (1, 1) | N -> let M0 = hailpair N in let M1 = largest (N - 1) in hailmax M0 M1 ]) using Systemusing Listusing Hailstone def task0 = let H27 = hailstone 27 in length H27 def task1 = let H27 = hailstone 27 in let L = length H27 in (take 4 H27, drop (L - 4) H27) def task2 = largest 100000 def main = (task0, task1, task2)  ## Eiffel  class APPLICATION create make feature make local test: LINKED_LIST [INTEGER] count, number, te: INTEGER do create test.make test := hailstone_sequence (27) io.put_string ("There are " + test.count.out + " elements in the sequence for the number 27.") io.put_string ("%NThe first 4 elements are: ") across 1 |..| 4 as t loop io.put_string (test [t.item].out + "%T") end io.put_string ("%NThe last 4 elements are: ") across (test.count - 3) |..| test.count as t loop io.put_string (test [t.item].out + "%T") end across 1 |..| 99999 as c loop test := hailstone_sequence (c.item) te := test.count if te > count then count := te number := c.item end end io.put_string ("%NThe longest sequence for numbers below 100000 is " + count.out + " for the number " + number.out + ".") end hailstone_sequence (n: INTEGER): LINKED_LIST [INTEGER] -- Members of the Hailstone Sequence starting from 'n'. require n_is_positive: n > 0 local seq: INTEGER do create Result.make from seq := n until seq = 1 loop Result.extend (seq) if seq \\ 2 = 0 then seq := seq // 2 else seq := ((3 * seq) + 1) end end Result.extend (seq) ensure sequence_terminated: Result.last = 1 end end  Output: There are 112 elements in the sequence for the number 27. The first 4 elements are: 27 82 41 124 The last 4 elements are: 8 4 2 1 The longest sequence for numbers below 100000 is 351 for the number 77031.  ## Elena ELENA 4.x : import system'collections;import extensions; const int maxNumber = 100000; Hailstone(int n,Map<int,int> lengths){ if (n == 1) { ^ 1 }; while (true) { if (lengths.containsKey(n)) { ^ lengths[n] } else { if (n.isEven()) { lengths[n] := 1 + Hailstone(n/2, lengths) } else { lengths[n] := 1 + Hailstone(3*n + 1, lengths) } } }} public program(){ int longestChain := 0; int longestNumber := 0; auto recursiveLengths := new Map<int,int>(4096,4096); for(int i := 1, i < maxNumber, i+=1) { var chainLength := Hailstone(i, recursiveLengths); if (longestChain < chainLength) { longestChain := chainLength; longestNumber := i } }; console.printFormatted("max below {0}: {1} ({2} steps)", maxNumber, longestNumber, longestChain)} Output: max bellow 100000: 77031 (351 steps)  ## Elixir defmodule Hailstone do require Integer def step(1) , do: 0 def step(n) when Integer.is_even(n), do: div(n,2) def step(n) , do: n*3 + 1 def sequence(n) do Stream.iterate(n, &step/1) |> Stream.take_while(&(&1 > 0)) |> Enum.to_list end def run do seq27 = sequence(27) len27 = length(seq27) repr = String.replace(inspect(seq27, limit: 4) <> inspect(Enum.drop(seq27,len27-4)), "][", ", ") IO.puts "Hailstone(27) has #{len27} elements: #{repr}" {len, start} = Enum.map(1..100_000, fn(n) -> {length(sequence(n)), n} end) |> Enum.max IO.puts "Longest sequence starting under 100000 begins with #{start} and has #{len} elements." endend Hailstone.run Output: Hailstone(27) has 112 elements: [27, 82, 41, 124, ..., 8, 4, 2, 1] Longest sequence starting under 100000 begins with 77031 and has 351 elements.  ## Erlang -module(hailstone).-import(io).-export([main/0]). hailstone(1) -> [1];hailstone(N) when N band 1 == 1 -> [N|hailstone(N * 3 + 1)];hailstone(N) when N band 1 == 0 -> [N|hailstone(N div 2)]. max_length(Start, Stop) -> F = fun (N) -> {length(hailstone(N)), N} end, Lengths = lists:map(F, lists:seq(Start, Stop)), lists:max(Lengths). main() -> io:format("hailstone(4): ~w~n", [hailstone(4)]), Seq27 = hailstone(27), io:format("hailstone(27) length: ~B~n", [length(Seq27)]), io:format("hailstone(27) first 4: ~w~n", [lists:sublist(Seq27, 4)]), io:format("hailstone(27) last 4: ~w~n", [lists:nthtail(length(Seq27) - 4, Seq27)]), io:format("finding maximum hailstone(N) length for 1 <= N <= 100000..."), {Length, N} = max_length(1, 100000), io:format(" done.~nhailstone(~B) length: ~B~n", [N, Length]). Output: Eshell V5.8.4 (abort with ^G) 1> c(hailstone). {ok,hailstone} 2> hailstone:main(). hailstone(4): [4,2,1] hailstone(27) length: 112 hailstone(27) first 4: [27,82,41,124] hailstone(27) last 4: [8,4,2,1] finding maximum hailstone(N) length for 1 <= N <= 100000... done. hailstone(77031) length: 351 ok Erlang 2 This version has one collatz function for just calculating totals (just for fun) and the second generating lists.  -module(collatz). -export([main/0,collatz/1,coll/1,max_atz_under/1]). collatz(1) -> 1; collatz(N) when N rem 2 == 0 -> 1 + collatz(N div 2); collatz(N) when N rem 2 > 0 -> 1 + collatz(3 * N +1). max_atz_under(N) -> F = fun (X) -> {collatz(X), X} end, {_, Index} = lists:max(lists:map(F, lists:seq(1, N))), Index. coll(1) -> [1]; coll(N) when N rem 2 == 0 -> [N|coll(N div 2)]; coll(N) -> [N|coll(3 * N + 1)]. main() -> io:format("collatz(4) non-list total: ~w~n", [collatz(4)]), io:format("coll(4) with lists ~w~n", [coll(4)] ), Seq27 = coll(27), Seq1000 = coll(max_atz_under(100000)), io:format("coll(27) length: ~B~n", [length(Seq27)]), io:format("coll(27) first 4: ~w~n", [lists:sublist(Seq27, 4)]), io:format("collatz(27) last 4: ~w~n", [lists:nthtail(length(Seq27) - 4, Seq27)]), io:format("maximum N <= 100000..."), io:format("Max: ~w~n", [max_atz_under(100000)]), io:format("Total: ~w~n", [ length( Seq1000 ) ] ).  Output 64> collatz:main(). collatz(4) non-list total: 3 coll(4) with lists [4,2,1] coll(27) length: 112 coll(27) first 4: [27,82,41,124] collatz(27) last 4: [8,4,2,1] maximum N <= 100000...Max: 77031 Total: 351 ok  ## ERRE In Italy it's known also as "Ulam conjecture".  PROGRAM ULAM !DOUBLE PROCEDURE HAILSTONE(X,PRT%->COUNT) COUNT=1 IF PRT% THEN PRINT(X,) END IF REPEAT IF X/2<>INT(X/2) THEN X=X*3+1 ELSE X=X/2 END IF IF PRT% THEN PRINT(X,) END IF COUNT=COUNT+1 UNTIL X=1 IF PRT% THEN PRINT END IFEND PROCEDURE BEGIN HAILSTONE(27,TRUE->COUNT) PRINT("Sequence length for 27:";COUNT) MAX_COUNT=2 NMAX=2 FOR I=3 TO 100000 DO HAILSTONE(I,FALSE->COUNT) IF COUNT>MAX_COUNT THEN NMAX=I MAX_COUNT=COUNT END IF END FOR PRINT("Max. number is";NMAX;" with";MAX_COUNT;"elements")END PROGRAM  Output:  27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Sequence length for 27: 112 Max. number is 77031 with 351 elements ## Euler Math Toolbox  >function hailstone (n) ... v=[n]; repeat if mod(n,2) then n=3*n+1; else n=n/2; endif; v=v|n; until n==1; end; return v; endfunction>hailstone(27), length(%) [ 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 ] 112>function hailstonelength (n) ... v=zeros(1,n); v[1]=4; v[2]=2; loop 3 to n; count=1; n=#; repeat if mod(n,2) then n=3*n+1; else n=n/2; endif; if n<=cols(v) and v[n] then  v[#]=v[n]+count; break; endif; count=count+1;  end; end; return v; endfunction>h=hailstonelength(100000);>ex=extrema(h); ex[3], ex[4] 351 77031  ## Euphoria function hailstone(atom n) sequence s s = {n} while n != 1 do if remainder(n,2)=0 then n /= 2 else n = 3*n + 1 end if s &= n end while return send function function hailstone_count(atom n) integer count count = 1 while n != 1 do if remainder(n,2)=0 then n /= 2 else n = 3*n + 1 end if count += 1 end while return countend function sequence ss = hailstone(27)puts(1,"hailstone(27) =\n")? sprintf(1,"len = %d\n\n",length(s)) integer max,imax,countmax = 0for i = 2 to 1e5-1 do count = hailstone_count(i) if count > max then max = count imax = i end ifend for printf(1,"The longest hailstone sequence under 100,000 is %d with %d elements.\n", {imax,max}) Output: hailstone(27) = {27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182, 91,274,137,412,206,103,310,155,466,233,700,350,175,526,263,790,395, 1186,593,1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283, 850,425,1276,638,319,958,479,1438,719,2158,1079,3238,1619,4858,2429, 7288,3644,1822,911,2734,1367,4102,2051,6154,3077,9232,4616,2308,1154, 577,1732,866,433,1300,650,325,976,488,244,122,61,184,92,46,23,70,35, 106,53,160,80,40,20,10,5,16,8,4,2,1} len = 112 The longest hailstone sequence under 100,000 is 77031 with 351 elements.  ## Excel  This example may be incorrect. Calculates the Hailstone sequence but might not complete everything from task description. Please verify it and remove this message. If the example does not match the requirements or does not work, replace this message with Template:incorrect or fix the code yourself.  In cell A1, place the starting number. In cell A2 enter this formula =IF(MOD(A1,2)=0,A1/2,A1*3+1) Drag and copy the formula down until 4, 2, 1  ## Ezhil Ezhil is a Tamil programming language, see | Wikipedia entry.  நிரல்பாகம் hailstone ( எண் ) பதிப்பி "=> ",எண் #hailstone seq @( எண் == 1 ) ஆனால் பின்கொடு எண் முடி @( (எண்%2) == 1 ) ஆனால் hailstone( 3*எண் + 1) இல்லை hailstone( எண்/2 ) முடிமுடி எண்கள் = [5,17,19,23,37]@(எண்கள் இல் இவ்வெண்) ஒவ்வொன்றாக பதிப்பி "****** calculating hailstone seq for ",இவ்வெண்," *********" hailstone( இவ்வெண் ) பதிப்பி "**********************************************"முடி  ## Factor ! rosetta/hailstone/hailstone.factorUSING: arrays io kernel math math.ranges prettyprint sequences vectors ;IN: rosetta.hailstone : hailstone ( n -- seq ) [ 1vector ] keep [ dup 1 number= ] [ dup even? [ 2 / ] [ 3 * 1 + ] if 2dup swap push ] until drop ; <PRIVATE: main ( -- ) 27 hailstone dup dup "The hailstone sequence from 27:" print " has length " write length . " starts with " write 4 head [ unparse ] map ", " join print " ends with " write 4 tail* [ unparse ] map ", " join print ! Maps n => { length n }, and reduces to longest Hailstone sequence. 1 100000 [a,b) [ [ hailstone length ] keep 2array ] [ [ [ first ] [email protected] > ] most ] map-reduce first2 "The hailstone sequence from " write pprint " has length " write pprint "." print ;PRIVATE> MAIN: main Output:  ./factor -run=rosetta.hailstone Loading resource:work/rosetta/hailstone/hailstone.factor The hailstone sequence from 27: has length 112 starts with 27, 82, 41, 124 ends with 8, 4, 2, 1 The hailstone sequence from 77031 has length 351. ## FALSE [1&[%3*1+0~]?~[2/]?]n:[[." "1>][n;!]#%]s:[1\[1>][\1+\n;!]#%]c:27s;! 27c;!.""0m:0f:1[100000\>][c;!m;>[m:f:0]?%1+]#%f;." has hailstone sequence length "m;. ## Fōrmulæ In this page you can see the solution of this task. Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition. The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code. ## Forth : hail-next ( n -- n ) dup 1 and if 3 * 1+ else 2/ then ;: .hail ( n -- ) begin dup . dup 1 > while hail-next repeat drop ;: hail-len ( n -- n ) 1 begin over 1 > while swap hail-next swap 1+ repeat nip ; 27 hail-len . cr27 .hail cr : longest-hail ( max -- ) 0 0 rot 1+ 1 do ( n length ) i hail-len 2dup < if nip nip i swap else drop then loop swap . ." has hailstone sequence length " . ; 100000 longest-hail ## Fortran Works with: Fortran version 95 and later program Hailstone implicit none integer :: i, maxn integer :: maxseqlen = 0, seqlen integer, allocatable :: seq(:) call hs(27, seqlen) allocate(seq(seqlen)) call hs(27, seqlen, seq) write(*,"(a,i0,a)") "Hailstone sequence for 27 has ", seqlen, " elements" write(*,"(a,4(i0,a),3(i0,a),i0)") "Sequence = ", seq(1), ", ", seq(2), ", ", seq(3), ", ", seq(4), " ...., ", & seq(seqlen-3), ", ", seq(seqlen-2), ", ", seq(seqlen-1), ", ", seq(seqlen) do i = 1, 99999 call hs(i, seqlen) if (seqlen > maxseqlen) then maxseqlen = seqlen maxn = i end if end do write(*,*) write(*,"(a,i0,a,i0,a)") "Longest sequence under 100000 is for ", maxn, " with ", maxseqlen, " elements" deallocate(seq) contains subroutine hs(number, length, seqArray) integer, intent(in) :: number integer, intent(out) :: length integer, optional, intent(inout) :: seqArray(:) integer :: n n = number length = 1 if(present(seqArray)) seqArray(1) = n do while(n /= 1) if(mod(n,2) == 0) then n = n / 2 else n = n * 3 + 1 end if length = length + 1 if(present(seqArray)) seqArray(length) = n end doend subroutine end program Output: Hailstone sequence for 27 has 112 elements Sequence = 27, 82, 41, 124, ...., 8, 4, 2, 1 Longest sequence under 100000 is for 77031 with 351 elements ## Frege Translation of: Haskell Works with: Frege version 3.21.586-g026e8d7 module Hailstone where import Data.List (maximumBy) hailstone :: Int -> [Int]hailstone 1 = [1]hailstone n | even n = n : hailstone (n div 2) | otherwise = n : hailstone (n * 3 + 1) withResult :: (t -> t1) -> t -> (t1, t)withResult f x = (f x, x) main :: IO ()main = do let h27 = hailstone 27 putStrLn  show  length h27 let h4 = show  take 4 h27 let t4 = show  drop (length h27 - 4) h27 putStrLn ("hailstone 27: " ++ h4 ++ " ... " ++ t4) putStrLn  show  maximumBy (comparing fst)  map (withResult (length . hailstone)) [1..100000] Output: 112 hailstone 27: [27, 82, 41, 124] ... [8, 4, 2, 1] (351, 77031) runtime 0.969 wallclock seconds.  ## Frink  hailstone[n] :={ results = new array while n != 1 { results.push[n] if n mod 2 == 0 // n is even? n = n / 2 else n = (3n + 1) } results.push[1] return results} longestLen = 0longestN = 0for n = 1 to 100000{ seq = hailstone[n] if length[seq] > longestLen { longestLen = length[seq] longestN = n }} println["longestN has length longestLen"]  ## F# let rec hailstone n = seq { match n with | 1 -> yield 1 | n when n % 2 = 0 -> yield n; yield! hailstone (n / 2) | n -> yield n; yield! hailstone (n * 3 + 1)} let hailstone27 = hailstone 27 |> Array.ofSeqassert (Array.length hailstone27 = 112)assert (hailstone27.[..3] = [|27;82;41;124|])assert (hailstone27.[108..] = [|8;4;2;1|]) let maxLen, maxI = Seq.max <| seq { for i in 1..99999 -> Seq.length (hailstone i), i}printfn "Maximum length %d was found for hailstone(%d)" maxLen maxI Output: Maximum length 351 was found for hailstone(77031) ## FunL def hailstone( 1 ) = [1] hailstone( n ) = n # hailstone( if 2|n then n/2 else n*3 + 1 ) if _name_ == '-main-' h27 = hailstone( 27 ) assert( h27.length() == 112 and h27.startsWith([27, 82, 41, 124]) and h27.endsWith([8, 4, 2, 1]) ) val (n, len) = maxBy( snd, [(i, hailstone( i ).length()) | i <- 1:100000] ) println( n, len ) Output: 77031, 351  ## Futhark  fun hailstone_step(x: int): int = if (x % 2) == 0 then x/2 else (3*x) + 1 fun hailstone_seq(x: int): []int = let capacity = 100 let i = 1 let steps = replicate capacity (-1) let steps[0] = x loop ((capacity,i,steps,x)) = while x != 1 do let (steps, capacity) = if i == capacity then (concat steps (replicate capacity (-1)), capacity * 2) else (steps, capacity) let x = hailstone_step x let steps[i] = x in (capacity, i+1, steps, x) in #1 (split i steps) fun hailstone_len(x: int): int = let i = 1 loop ((i,x)) = while x != 1 do (i+1, hailstone_step x) in i fun max (x: int) (y: int): int = if x < y then y else x fun main (x: int) (n: int): ([]int, int) = (hailstone_seq x, reduce max 0 (map hailstone_len (map (1+) (iota (n-1)))))  ## GAP CollatzSequence := function(n) local v; v := [ n ]; while n > 1 do if IsEvenInt(n) then n := QuoInt(n, 2); else n := 3*n + 1; fi; Add(v, n); od; return v;end; CollatzLength := function(n) local m; m := 1; while n > 1 do if IsEvenInt(n) then n := QuoInt(n, 2); else n := 3*n + 1; fi; m := m + 1; od; return m;end; CollatzMax := function(a, b) local n, len, nmax, lmax; lmax := 0; for n in [a .. b] do len := CollatzLength(n); if len > lmax then nmax := n; lmax := len; fi; od; return [ nmax, lmax ];end; CollatzSequence(27);# [ 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, # 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, # 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, # 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, # 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1 ]CollatzLength(27); # 112 CollatzMax(1, 100);# [ 97, 119 ]CollatzMax(1, 1000);# [ 871, 179 ]CollatzMax(1, 10000);# [ 6171, 262 ]CollatzMax(1, 100000);# [ 77031, 351 ]CollatzMax(1, 1000000);# [ 837799, 525 ] ## Go package main import "fmt" // 1st arg is the number to generate the sequence for.// 2nd arg is a slice to recycle, to reduce garbage.func hs(n int, recycle []int) []int { s := append(recycle[:0], n) for n > 1 { if n&1 == 0 { n = n / 2 } else { n = 3*n + 1 } s = append(s, n) } return s} func main() { seq := hs(27, nil) fmt.Printf("hs(27): %d elements: [%d %d %d %d ... %d %d %d %d]\n", len(seq), seq[0], seq[1], seq[2], seq[3], seq[len(seq)-4], seq[len(seq)-3], seq[len(seq)-2], seq[len(seq)-1]) var maxN, maxLen int for n := 1; n < 100000; n++ { seq = hs(n, seq) if len(seq) > maxLen { maxN = n maxLen = len(seq) } } fmt.Printf("hs(%d): %d elements\n", maxN, maxLen)} Output: hs(27): 112 elements: [27 82 41 124 ... 8 4 2 1] hs(77031): 351 elements  Alternate solution (inspired both by recent news of a new proof submitted for publication and by recent chat on #rosettacode about generators.) This solution interprets the wording of the task differently, and takes the word "generate" to mean use a generator. This has the advantage of not storing the whole sequence in memory at once. Elements are generated one at a time, counted and discarded. A time optimization added for task 3 is to store the sequence lengths computed so far. Output is the same as version above. package main import "fmt" // Task 1 implemented with a generator. Calling newHg will "create// a routine to generate the hailstone sequence for a number."func newHg(n int) func() int { return func() (n0 int) { n0 = n if n&1 == 0 { n = n / 2 } else { n = 3*n + 1 } return }} func main() { // make generator for sequence starting at 27 hg := newHg(27) // save first four elements for printing later s1, s2, s3, s4 := hg(), hg(), hg(), hg() // load next four elements in variables to use as shift register. e4, e3, e2, e1 := hg(), hg(), hg(), hg() // 4+4= 8 that we've generated so far ec := 8 // until we get to 1, generate another value, shift, and increment. // note that intermediate elements--those shifted off--are not saved. for e1 > 1 { e4, e3, e2, e1 = e3, e2, e1, hg() ec++ } // Complete task 2: fmt.Printf("hs(27): %d elements: [%d %d %d %d ... %d %d %d %d]\n", ec, s1, s2, s3, s4, e4, e3, e2, e1) // Task 3: strategy is to not store sequences, but just the length // of each sequence. as soon as the sequence we're currently working on // dips into the range that we've already computed, we short-circuit // to the end by adding the that known length to whatever length // we've accumulated so far. var nMaxLen int // variable holds n with max length encounted so far // slice holds sequence length for each n as it is computed var computedLen [1e5]int computedLen[1] = 1 for n := 2; n < 1e5; n++ { var ele, lSum int for hg := newHg(n); ; lSum++ { ele = hg() // as soon as we get an element in the range we have already // computed, we're done... if ele < n { break } } // just add the sequence length already computed from this point. lSum += computedLen[ele] // save the sequence length for this n computedLen[n] = lSum // and note if it's the maximum so far if lSum > computedLen[nMaxLen] { nMaxLen = n } } fmt.Printf("hs(%d): %d elements\n", nMaxLen, computedLen[nMaxLen])} ## Groovy def hailstone = { long start -> def sequence = [] while (start != 1) { sequence << start start = (start % 2l == 0l) ? start / 2l : 3l * start + 1l } sequence << start} Test Code def sequence = hailstone(27)assert sequence.size() == 112assert sequence[0..3] == [27, 82, 41, 124]assert sequence[-4..-1] == [8, 4, 2, 1] def results = (1..100000).collect { [n:it, size:hailstone(it).size()] }.max { it.size }println results Output: [n:77031, size:351] ## Haskell import Data.List (maximumBy)import Data.Ord (comparing) collatz :: Int -> Intcollatz n | even n = n div 2 | otherwise = 3 * n + 1 hailstone :: Int -> [Int]hailstone = takeWhile (/= 1) . iterate collatz longestChain :: IntlongestChain = fst  maximumBy (comparing snd)  (,) <*> (length . hailstone) <> [1 .. 100000] --TEST -------------------------------------------------------------------------main :: IO ()main = mapM_ putStrLn [ "Collatz sequence for 27: " , (show . hailstone) 27 , "The number " ++ show longestChain , "has the longest hailstone sequence for any number less then 100000. " , "The sequence has length: " ++ (show . length . hailstone  longestChain) ] Output: Collatz sequence for 27: [27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,91,274,137,412,206,103,310,155,466,233,700,350,175,526,263,790,395,1186,593,1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283,850,425,1276,638,319,958,479,1438,719,2158,1079,3238,1619,4858,2429,7288,3644,1822,911,2734,1367,4102,2051,6154,3077,9232,4616,2308,1154,577,1732,866,433,1300,650,325,976,488,244,122,61,184,92,46,23,70,35,106,53,160,80,40,20,10,5,16,8,4,2] The number 77031 has the longest hailstone sequence for any number less then 100000. The sequence has length: 350 The following is an older version, which some of the language examples on this page are translated from: import Data.Ord (comparing)import Data.List (maximumBy, intercalate) hailstone :: Int -> [Int]hailstone 1 = [1]hailstone n | even n = n : hailstone (n div 2) | otherwise = n : hailstone (n * 3 + 1) withResult :: (Int -> Int) -> Int -> (Int, Int)withResult f x = (f x, x) h27 :: [Int]h27 = hailstone 27 main :: IO ()main = mapM_ putStrLn [ (show . length) h27 , "hailstone 27: " ++ intercalate " ... " (show <> [take 4 h27, drop (length h27 - 4) h27]) , show  maximumBy (comparing fst)  withResult (length . hailstone) <> [1 .. 100000] ] Output: 112 hailstone 27: [27,82,41,124] ... [8,4,2,1] (351,77031) Or, going back to basics, we can observe that the hailstone sequence is an 'anamorphism' – it builds up a list structure from a single integer value, which makes unfoldr the obvious first thing to reach for the first main task. In turn, deriving the longest sequence for starting values below 100000 essentially involves a 'catamorphism' – it takes a list of hailstone sequences (or at least a list of their seed values and their lengths), and strips that structure down to a single (N, length) pair. This makes foldr the obvious recursion scheme to start with for the second main task. One approach to using unfoldr and then foldr might be: import Data.List (unfoldr) hailStones :: Int -> [Int]hailStones = (++ [1]) . unfoldr (\x -> if x < 2 then Nothing else Just ( x , if even x then div x 2 else (3 * x) + 1)) mostStones :: Int -> (Int, Int)mostStones n = foldr (\x (m, ml) -> let l = length (hailStones x) in if l > ml then (x, l) else (m, ml)) (0, 0) [1 .. n] -- GENERIC -------------------------------------------------------------------lastN_ :: Int -> [Int] -> [Int]lastN_ = (foldr (const (drop 1)) <*>) . drop -- TEST -----------------------------------------------------------------------h27, start27, end27 :: [Int][h27, start27, end27] = [id, take 4, lastN_ 4] <*> [hailStones 27] maxNum, maxLen :: Int(maxNum, maxLen) = mostStones 100000 main :: IO ()main = mapM_ putStrLn [ "Sequence 27 length:" , show  length h27 , "Sequence 27 start:" , show start27 , "Sequence 27 end:" , show end27 , "" , "N with longest sequence where N <= 100000" , show maxNum , "length of this sequence:" , show maxLen ] Output: Sequence 27 length: 112 Sequence 27 start: [27,82,41,124] Sequence 27 end: [8,4,2,1] N with longest sequence where N <= 100000 77031 length of this sequence: 351 ## HicEst DIMENSION stones(1000) H27 = hailstone(27)ALIAS(stones,1, first4,4)ALIAS(stones,H27-3, last4,4)WRITE(ClipBoard, Name) H27, first4, "...", last4 longest_sequence = 0DO try = 1, 1E5 elements = hailstone(try) IF(elements >= longest_sequence) THEN number = try longest_sequence = elements WRITE(StatusBar, Name) number, longest_sequence ENDIFENDDOWRITE(ClipBoard, Name) number, longest_sequenceEND FUNCTION hailstone( n ) USE : stones stones(1) = n DO i = 1, LEN(stones) IF(stones(i) == 1) THEN hailstone = i RETURN ELSEIF( MOD(stones(i),2) ) THEN stones(i+1) = 3*stones(i) + 1 ELSE stones(i+1) = stones(i) / 2 ENDIF ENDDOEND H27=112; first4(1)=27; first4(2)=82; first4(3)=41; first4(4)=124; ...; last4(1)=8; last4(2)=4; last4(3)=2; last4(4)=1; number=77031; longest_sequence=351; ## Icon and Unicon A simple solution that generates (in the Icon sense) the sequence is: procedure hailstone(n) while n > 1 do { suspend n n := if n%2 = 0 then n/2 else 3*n+1 } suspend 1end and a test program for this solution is: procedure main(args) n := integer(!args) | 27 every writes(" ",hailstone(n))end but this solution is computationally expensive when run repeatedly (task 3). The following solution uses caching to improve performance on task 3 at the expense of space. procedure hailstone(n) static cache initial { cache := table() cache[1] := [1] } /cache[n] := [n] ||| hailstone(if n%2 = 0 then n/2 else 3*n+1) return cache[n]end A test program is: procedure main(args) n := integer(!args) | 27 task2(n) write() task3()end procedure task2(n) count := 0 every writes(" ",right(!(sequence := hailstone(n)),5)) do if (count +:= 1) % 15 = 0 then write() write() write(*sequence," value",(*sequence=1,"")|"s"," in the sequence.")end procedure task3() maxHS := 0 every n := 1 to 100000 do { count := *hailstone(n) if maxHS <:= count then maxN := n } write(maxN," has a sequence of ",maxHS," values")end A sample run is: ->hs 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 112 values in the sequence. 77031 has a sequence of 351 values ->  ## Io Here is a simple, brute-force approach:  makeItHail := method(n, stones := list(n) while (n != 1, if(n isEven, n = n / 2, n = 3 * n + 1 ) stones append(n) ) stones) out := makeItHail(27)writeln("For the sequence beginning at 27, the number of elements generated is ", out size, ".")write("The first four elements generated are ")for(i, 0, 3, write(out at(i), " "))writeln(".") write("The last four elements generated are ")for(i, out size - 4, out size - 1, write(out at(i), " "))writeln(".") numOfElems := 0nn := 3for(x, 3, 100000, out = makeItHail(x) if(out size > numOfElems, numOfElems = out size nn = x )) writeln("For numbers less than or equal to 100,000, ", nn," has the longest sequence of ", numOfElems, " elements.")  Output: For the sequence beginning at 27, the number of elements generated is 112. The first four elements generated are 27 82 41 124 . The last four elements generated are 8 4 2 1 . For numbers less than or equal to 100,000, 77031 has the longest sequence of 351 elements.  ## Ioke  This example may be incorrect. Calculates the Hailstone sequence but might not complete everything from task description. Please verify it and remove this message. If the example does not match the requirements or does not work, replace this message with Template:incorrect or fix the code yourself. collatz = method(n, n println unless(n <= 1, if(n even?, collatz(n / 2), collatz(n * 3 + 1)))) ## Inform 7 This solution uses a cache to speed up the length calculation for larger numbers. Home is a room. To decide which list of numbers is the hailstone sequence for (N - number): let result be a list of numbers; add N to result; while N is not 1: if N is even, let N be N / 2; otherwise let N be (3 * N) + 1; add N to result; decide on result. Hailstone length cache relates various numbers to one number. To decide which number is the hailstone sequence length for (N - number): let ON be N; let length so far be 0; while N is not 1: if N relates to a number by the hailstone length cache relation: let result be length so far plus the number to which N relates by the hailstone length cache relation; now the hailstone length cache relation relates ON to result; decide on result; if N is even, let N be N / 2; otherwise let N be (3 * N) + 1; increment length so far; let result be length so far plus 1; now the hailstone length cache relation relates ON to result; decide on result. To say first and last (N - number) entry/entries in (L - list of values of kind K): let length be the number of entries in L; if length <= N * 2: say L; else: repeat with M running from 1 to N: if M > 1, say ", "; say entry M in L; say " ... "; repeat with M running from length - N + 1 to length: say entry M in L; if M < length, say ", ". When play begins: let H27 be the hailstone sequence for 27; say "Hailstone sequence for 27 has [number of entries in H27] element[s]: [first and last 4 entries in H27]."; let best length be 0; let best number be 0; repeat with N running from 1 to 99999: let L be the hailstone sequence length for N; if L > best length: let best length be L; let best number be N; say "The number under 100,000 with the longest hailstone sequence is [best number] with [best length] element[s]."; end the story. Output: Hailstone sequence for 27 has 112 elements: 27, 82, 41, 124 ... 8, 4, 2, 1. The number under 100,000 with the longest hailstone sequence is 77031 with 351 elements. ## J Solution: hailseq=: -:(1 3&p.)@.(2&|) ^:(1 ~: ]) ^:a:"0 Usage:  # hailseq 27 NB. sequence length112 4 _4 {."0 1 hailseq 27 NB. first & last 4 numbers in sequence27 82 41 124 8 4 2 1 (>:@(i. >./) , >./) #@hailseq }.i. 1e5 NB. number < 100000 with max seq length & its seq length77031 351 See also the Collatz Conjecture essay on the J wiki. ## Java Works with: Java version 1.5+ import java.util.ArrayList;import java.util.HashMap;import java.util.List;import java.util.Map; class Hailstone { public static List<Long> getHailstoneSequence(long n) { if (n <= 0) throw new IllegalArgumentException("Invalid starting sequence number"); List<Long> list = new ArrayList<Long>(); list.add(Long.valueOf(n)); while (n != 1) { if ((n & 1) == 0) n = n / 2; else n = 3 * n + 1; list.add(Long.valueOf(n)); } return list; } public static void main(String[] args) { List<Long> sequence27 = getHailstoneSequence(27); System.out.println("Sequence for 27 has " + sequence27.size() + " elements: " + sequence27); long MAX = 100000; // Simple way { long highestNumber = 1; int highestCount = 1; for (long i = 2; i < MAX; i++) { int count = getHailstoneSequence(i).size(); if (count > highestCount) { highestCount = count; highestNumber = i; } } System.out.println("Method 1, number " + highestNumber + " has the longest sequence, with a length of " + highestCount); } // More memory efficient way { long highestNumber = 1; int highestCount = 1; for (long i = 2; i < MAX; i++) { int count = 1; long n = i; while (n != 1) { if ((n & 1) == 0) n = n / 2; else n = 3 * n + 1; count++; } if (count > highestCount) { highestCount = count; highestNumber = i; } } System.out.println("Method 2, number " + highestNumber + " has the longest sequence, with a length of " + highestCount); } // Efficient for analyzing all sequences { long highestNumber = 1; long highestCount = 1; Map<Long, Integer> sequenceMap = new HashMap<Long, Integer>(); sequenceMap.put(Long.valueOf(1), Integer.valueOf(1)); List<Long> currentList = new ArrayList<Long>(); for (long i = 2; i < MAX; i++) { currentList.clear(); Long n = Long.valueOf(i); Integer count = null; while ((count = sequenceMap.get(n)) == null) { currentList.add(n); long nValue = n.longValue(); if ((nValue & 1) == 0) n = Long.valueOf(nValue / 2); else n = Long.valueOf(3 * nValue + 1); } int curCount = count.intValue(); for (int j = currentList.size() - 1; j >= 0; j--) sequenceMap.put(currentList.get(j), Integer.valueOf(++curCount)); if (curCount > highestCount) { highestCount = curCount; highestNumber = i; } } System.out.println("Method 3, number " + highestNumber + " has the longest sequence, with a length of " + highestCount); } return; }} Output: Sequence for 27 has 112 elements: [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1] Method 1, number 77031 has the longest sequence, with a length of 351 Method 2, number 77031 has the longest sequence, with a length of 351 Method 3, number 77031 has the longest sequence, with a length of 351  ## JavaScript ### ES5 #### Imperative function hailstone (n) { var seq = [n]; while (n > 1) { n = n % 2 ? 3 * n + 1 : n / 2; seq.push(n); } return seq;} // task 2: verify the sequence for n = 27var h = hailstone(27), hLen = h.length;print("sequence 27 is (" + h.slice(0, 4).join(", ") + " ... " + h.slice(hLen - 4, hLen).join(", ") + "). length: " + hLen); // task 3: find the longest sequence for n < 100000for (var n, max = 0, i = 100000; --i;) { var seq = hailstone(i), sLen = seq.length; if (sLen > max) { n = i; max = sLen; }}print("longest sequence: " + max + " numbers for starting point " + n); Output: sequence 27 is (27, 82, 41, 124 ... 8, 4, 2, 1). length: 112 longest sequence: 351 numbers for starting point 77031 #### Functional This simple problem turns out to be a good test of the constraints on composing (ES5) JavaScript code in a functional style. The first sub-problem falls easily within reach of a basic recursive definition (translating one of the Haskell solutions). (function () { // Hailstone Sequence // n -> [n] function hailstone(n) { return n === 1 ? [1] : ( [n].concat( hailstone(n % 2 ? n * 3 + 1 : n / 2) ) ) } var lstCollatz27 = hailstone(27); return { length: lstCollatz27.length, sequence: lstCollatz27 }; })(); Output: {"length":112,"sequence":[27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,91,274,137,412,206,103,310,155,466,233,700,350,175,526, 263,790,395,1186,593,1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283,850,425,1276,638,319,958,479,1438,719,2158,1079,3238,1619,4858,2429,7288,3644,1822,911,2734,1367,4102,2051,6154,3077,9232,4616,2308,1154,577,1732,866,433,1300,650,325,976,488,244,122,61,184,92,46,23,70,35,106,53,160,80,40,20,10,5,16,8,4,2,1]} Attempting to fold that recursive function over an array of 100,000 elements, however, (to solve the second part of the problem) soon runs out of stack space, at least on the system used here. The stack problem can be quickly fixed, as often, by simply applying a memoized function, which reuses previously calculated paths. (function () { function memoizedHailstone() { var dctMemo = {}; return function hailstone(n) { var value = dctMemo[n]; if (typeof value === "undefined") { dctMemo[n] = value = (n === 1) ? [1] : ([n].concat(hailstone(n % 2 ? n * 3 + 1 : n / 2))); } return value; } } // Derived a memoized version of the function, // which can reuse previously calculated paths var fnCollatz = memoizedHailstone(); // Iterative version of range // [m..n] function range(m, n) { var a = Array(n - m + 1), i = n + 1; while (i--) a[i - 1] = i; return a; } // Fold/reduce over an array to find the maximum length function longestBelow(n) { return range(1, n).reduce( function (a, x, i) { var lng = fnCollatz(x).length; return lng > a.l ? { n: i + 1, l: lng } : a }, { n: 0, l: 0 } ) } return longestBelow(100000); })(); Output: // Number, length of sequence{"n":77031, "l":351} For better time (as well as space) we can continue to memoize while falling back to a function which returns the sequence length alone, and is iteratively implemented. This also proves more scaleable, and we can still use a fold/reduce pattern over a list to find the longest collatz sequences for integers below one million, or ten million and beyond, without hitting the limits of system resources. (function (n) { var dctMemo = {}; // Length only of hailstone sequence // n -> n function collatzLength(n) { var i = 1, a = n, lng; while (a !== 1) { lng = dctMemo[a]; if ('u' === (typeof lng)[0]) { a = (a % 2 ? 3 * a + 1 : a / 2); i++; } else return lng + i - 1; } return i; } // Iterative version of range // [m..n] function range(m, n) { var a = Array(n - m + 1), i = n + 1; while (i--) a[i - 1] = i; return a; } // Fold/reduce over an array to find the maximum length function longestBelow(n) { return range(1, n).reduce( function (a, x) { var lng = dctMemo[x] || (dctMemo[x] = collatzLength(x)); return lng > a.l ? { n: x, l: lng } : a }, { n: 0, l: 0 } ) } return [100000, 1000000, 10000000].map(longestBelow); })(); Output: [ {"n":77031, "l":351}, // 100,000 {"n":837799, "l":525}, // 1,000,000 {"n":8400511, "l":686} // 10,000,000] longestBelow(100000000)-> {"n":63728127, "l":950} ### ES6 (() => { // hailstones :: Int -> [Int] const hailstones = x => { const collatz = memoized(n => even(n) ? div(n, 2) : (3 * n) + 1); return reverse(until( xs => xs[0] === 1, xs => cons(collatz(xs[0]), xs), [x] )); }; // collatzLength :: Int -> Int const collatzLength = n => until( xi => xi[0] === 1, ([x, i]) => [(x % 2 ? 3 * x + 1 : x / 2), i + 1], // [n, 1] )[1]; // GENERIC FUNCTIONS ----------------------------------------------------- // comparing :: (a -> b) -> (a -> a -> Ordering) const comparing = f => (x, y) => { const a = f(x), b = f(y); return a < b ? -1 : (a > b ? 1 : 0); }; // cons :: a -> [a] -> [a] const cons = (x, xs) => [x].concat(xs); // div :: Int -> Int -> Int const div = (x, y) => Math.floor(x / y); // enumFromTo :: Int -> Int -> [Int] const enumFromTo = (m, n) => Array.from({ length: Math.floor(n - m) + 1 }, (_, i) => m + i); // even :: Int -> Bool const even = n => n % 2 === 0; // fst :: (a, b) -> a const fst = pair => pair.length === 2 ? pair[0] : undefined; // map :: (a -> b) -> [a] -> [b] const map = (f, xs) => xs.map(f); // maximumBy :: (a -> a -> Ordering) -> [a] -> a const maximumBy = (f, xs) => xs.length > 0 ? ( xs.slice(1) .reduce((a, x) => f(x, a) > 0 ? x : a, xs[0]) ) : undefined; // memoized :: (a -> b) -> (a -> b) const memoized = f => { const dctMemo = {}; return x => { const v = dctMemo[x]; return v !== undefined ? v : (dctMemo[x] = f(x)); }; }; // reverse :: [a] -> [a] const reverse = xs => xs.slice(0) .reverse(); // unlines :: [String] -> String const unlines = xs => xs.join('\n'); // until :: (a -> Bool) -> (a -> a) -> a -> a const until = (p, f, x) => { let v = x; while (!p(v)) v = f(v); return v; }; // MAIN ------------------------------------------------------------------ const // ceiling :: Int ceiling = 100000, // (maxLen, maxNum) :: (Int, Int) [maxLen, maxNum] = maximumBy( comparing(fst), map(i => [collatzLength(i), i], enumFromTo(1, ceiling)) ); return unlines([ 'Collatz sequence for 27: ', {hailstones(27)}, '', The number {maxNum} has the longest hailstone sequence, for any starting number under {ceiling}., '', The length of that sequence is {maxLen}. ]);})(); Output: (Run in the Atom editor, through the Script package) Collatz sequence for 27: 27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,91, 274,137,412,206,103,310,155,466,233,700,350,175,526,263,790,395,1186,593, 1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283,850,425,1276, 638,319,958,479,1438,719,2158,1079,3238,1619,4858,2429,7288,3644,1822, 911,2734,1367,4102,2051,6154,3077,9232,4616,2308,1154,577,1732,866,433, 1300,650,325,976,488,244,122,61,184,92,46,23,70,35,106,53,160,80,40,20, 10,5,16,8,4,2,1 The number 77031 has the longest hailstone sequence for any starting number under 100000. The length of that sequence is 351. [Finished in 1.139s]  ## jq Works with: jq version 1.4 # Generate the hailstone sequence as a stream to save space (and time) when countingdef hailstone: recurse( if . > 1 then if . % 2 == 0 then ./2|floor else 3*. + 1 end else empty end ); def count(g): reduce g as i (0; .+1); # return [i, length] for the first maximal-length hailstone sequence where i is in [1 .. n]def max_hailstone(n): # state: [i, length] reduce range(1; n+1) as i ([0,0]; (i | count(hailstone)) as l | if l > .[1] then [i, l] else . end); Examples: [27|hailstone] as h| "[27|hailstone]|length is \(h|length)", "The first four numbers: \(h[0:4])", "The last four numbers: \(h|.[length-4:length])", "", max_hailstone(100000) as m | "Maximum length for n|hailstone for n in 1..100000 is \(m[1]) (n == \(m[0]))" Output:  jq -M -r -n -f hailstone.jq[27|hailstone]|length is 112The first four numbers: [27,82,41,124]The last four numbers: [8,4,2,1] Maximum length for n|hailstone for n in 1..100000 is 351 (n == 77031) ## Julia Works with: Julia version 0.6 and 1.0+ ### Dynamic solution function hailstonelength(n::Integer) len = 1 while n > 1 n = ifelse(iseven(n), n ÷ 2, 3n + 1) len += 1 end return lenend @show hailstonelength(27); nothing@show findmax([hailstonelength(i) for i in 1:100_000]); nothing Output: hailstonelength(27) = 112 findmax((hailstonelength(i) for i = 1:100000)) = (351, 77031)  ### Solution with iterator #### Julia 1.0 Works with: Julia version 1.0+ struct HailstoneSeq{T<:Integer} count::Tend Base.eltype(::HailstoneSeq{T}) where T = T function Base.iterate(h::HailstoneSeq, state=h.count) if state == 1 (1, 0) elseif state < 1 nothing elseif iseven(state) (state, state ÷ 2) elseif isodd(state) (state, 3state + 1) endend function Base.length(h::HailstoneSeq) len = 0 for _ in h len += 1 end return lenend function Base.show(io::IO, h::HailstoneSeq) f5 = collect(Iterators.take(h, 5)) print(io, "HailstoneSeq{", join(f5, ", "), "...}")end hs = HailstoneSeq(27)println("Collection of the Hailstone sequence from 27: hs")cl = collect(hs)println("First 5 elements: ", join(cl[1:5], ", "))println("Last 5 elements: ", join(cl[end-4:end], ", ")) Base.isless(h::HailstoneSeq, s::HailstoneSeq) = length(h) < length(s)println("The number with the longest sequence under 100,000 is: ", maximum(HailstoneSeq.(1:100_000))) Output: Collection of the Hailstone sequence from 27: HailstoneSeq{27, 82, 411, 124, 62...} First 5 elements: 27, 82, 41, 124, 62 Last 5 elements: 16, 8, 4, 2, 1 The number with the longest sequence under 100,000 is: HailstoneSeq{777031, 231094, 115547, 346642, 173321...} #### Julia 0.6 Works with: Julia version 0.6 struct HailstoneSeq{T<:Integer} start::Tend Base.eltype(::HailstoneSeq{T}) where T = T Base.start(hs::HailstoneSeq) = (-1, hs.start)Base.done(::HailstoneSeq, state) = state == (1, 4)function Base.next(::HailstoneSeq, state) _, s2 = state s1 = s2 if iseven(s2) s2 = s2 ÷ 2 else s2 = 3s2 + 1 end return s1, (s1, s2)end function Base.length(hs::HailstoneSeq) r = 0 for _ in hs r += 1 end return rend function Base.show(io::IO, hs::HailstoneSeq) f5 = collect(Iterators.take(hs, 5)) print(io, "HailstoneSeq(", join(f5, ", "), "...)")end hs = HailstoneSeq(27)println("Collection of the Hailstone sequence from 27: hs")cl = collect(hs)println("First 5 elements: ", join(cl[1:5], ", "))println("Last 5 elements: ", join(cl[end-4:end], ", ")) Base.isless(h::HailstoneSeq, s::HailstoneSeq) = length(h) < length(s)println("The number with the longest sequence under 100,000 is: ", maximum(HailstoneSeq.(1:100_000))) Output: Collection of the Hailstone sequence from 27: HailstoneSeq(27, 82, 41, 124, 62...) First 5 elements: 27, 82, 41, 124, 62 Last 5 elements: 16, 8, 4, 2, 1 The number with the longest sequence under 100,000 is: HailstoneSeq(77031, 231094, 115547, 346642, 173321...) ## K  hail: (1<){:[x!2;1+3*x;_ x%2]}\ seqn: hail 27 #seqn112 4#seqn27 82 41 124 -4#seqn8 4 2 1 {m,[email protected]?m:|/s:{#hail x}'x}{[email protected]&x!2}!:1e5351 77031 ## Kotlin import java.util.ArrayDeque fun hailstone(n: Int): ArrayDeque<Int> { val hails = when { n == 1 -> ArrayDeque<Int>() n % 2 == 0 -> hailstone(n / 2) else -> hailstone(3 * n + 1) } hails.addFirst(n) return hails} fun main(args: Array<String>) { val hail27 = hailstone(27) fun showSeq(s: List<Int>) = s.map { it.toString() }.reduce { a, b -> a + ", " + b } println("Hailstone sequence for 27 is " + showSeq(hail27.take(3)) + " ... " + showSeq(hail27.drop(hail27.size - 3)) + " with length {hail27.size}.") var longestHail = hailstone(1) for (x in 1..99999) longestHail = arrayOf(hailstone(x), longestHail).maxBy { it.size } ?: longestHail println("{longestHail.first} is the number less than 100000 with " + "the longest sequence, having length {longestHail.size}.")} Output: Hailstone sequence for 27 is 27, 82, 41 ... 4, 2, 1 with length 112. 77031 is the number less than 100000 with the longest sequence, having length 351. ## Lasso [ define_tag("hailstone", -required="n", -type="integer", -copy); local("sequence") = array(#n); while(#n != 1); ((#n % 2) == 0) ? #n = (#n / 2) | #n = (#n * 3 + 1); #sequence->insert(#n); /while; return(#sequence); /define_tag; local("result"); #result = hailstone(27); while(#result->size > 8); #result->remove(5); /while; #result->insert("...",5); "Hailstone sequence for n = 27 -> { " + #result->join(", ") + " }"; local("longest_sequence") = 0; local("longest_index") = 0; loop(-from=1, -to=100000); local("length") = hailstone(loop_count)->size; if(#length > #longest_sequence); #longest_index = loop_count; #longest_sequence = #length; /if; /loop; "<br/>"; "Number with the longest sequence under 100,000: " #longest_index + ", with " + #longest_sequence + " elements.";] ## Logo to hail.next :n output ifelse equal? 0 modulo :n 2 [:n/2] [3*:n + 1]end to hail.seq :n if :n = 1 [output [1]] output fput :n hail.seq hail.next :nend show hail.seq 27show count hail.seq 27 to max.hail :n localmake "max.n 0 localmake "max.length 0 repeat :n [if greater? count hail.seq repcount :max.length [ make "max.n repcount make "max.length count hail.seq repcount ] ] (print :max.n [has hailstone sequence length] :max.length)end max.hail 100000 ## Limbo implement Hailstone; include "sys.m"; sys: Sys;include "draw.m"; Hailstone: module { init: fn(ctxt: ref Draw->Context, args: list of string);}; init(nil: ref Draw->Context, nil: list of string){ sys = load Sys Sys->PATH; seq := hailstone(big 27); l := len seq; sys->print("hailstone(27): "); for(i := 0; i < 4; i++) { sys->print("%bd, ", hd seq); seq = tl seq; } sys->print("⋯"); while(len seq > 4) seq = tl seq; while(seq != nil) { sys->print(", %bd", hd seq); seq = tl seq; } sys->print(" (length %d)\n", l); max := 1; maxn := big 1; for(n := big 2; n < big 100000; n++) { cur := len hailstone(n); if(cur > max) { max = cur; maxn = n; } } sys->print("hailstone(%bd) has length %d\n", maxn, max);} hailstone(i: big): list of big{ if(i == big 1) return big 1 :: nil; if(i % big 2 == big 0) return i :: hailstone(i / big 2); return i :: hailstone((big 3 * i) + big 1);}  Output: hailstone(27): 27, 82, 41, 124, ⋯, 8, 4, 2, 1 (length 112) hailstone(77031) has length 351  ## Lingo on hailstone (n, sequenceList) len = 1 repeat while n<>1 if listP(sequenceList) then sequenceList.add(n) if n mod 2 = 0 then n = n / 2 else n = 3 * n + 1 end if len = len + 1 end repeat if listP(sequenceList) then sequenceList.add(n) return lenend Usage: sequenceList = []hailstone(27, sequenceList)put sequenceList-- [27, 82, 41, 124, ... , 8, 4, 2, 1] n = 0maxLen = 0repeat with i = 1 to 99999 len = hailstone(i) if len>maxLen then n = i maxLen = len end ifend repeatput n, maxLen-- 77031 351 ## Logtalk :- object(hailstone). :- public(generate_sequence/2). :- mode(generate_sequence(+natural, -list(natural)), zero_or_one). :- info(generate_sequence/2, [ comment is 'Generates the Hailstone sequence that starts with its first argument. Fails if the argument is not a natural number.', argnames is ['Start', 'Sequence'] ]). :- public(write_sequence/1). :- mode(write_sequence(+natural), zero_or_one). :- info(write_sequence/1, [ comment is 'Writes to the standard output the Hailstone sequence that starts with its argument. Fails if the argument is not a natural number.', argnames is ['Start'] ]). :- public(sequence_length/2). :- mode(sequence_length(+natural, -natural), zero_or_one). :- info(sequence_length/2, [ comment is 'Calculates the length of the Hailstone sequence that starts with its first argument. Fails if the argument is not a natural number.', argnames is ['Start', 'Length'] ]). :- public(longest_sequence/4). :- mode(longest_sequence(+natural, +natural, -natural, -natural), zero_or_one). :- info(longest_sequence/4, [ comment is 'Calculates the longest Hailstone sequence in the interval [Start, End]. Fails if the interval is not valid.', argnames is ['Start', 'End', 'N', 'Length'] ]). generate_sequence(Start, Sequence) :- integer(Start), Start >= 1, sequence(Start, Sequence). sequence(1, [1]) :- !. sequence(N, [N| Sequence]) :- ( N mod 2 =:= 0 -> M is N // 2 ; M is (3 * N) + 1 ), sequence(M, Sequence). write_sequence(Start) :- integer(Start), Start >= 1, sequence(Start). sequence(1) :- !, write(1), nl. sequence(N) :- write(N), write(' '), ( N mod 2 =:= 0 -> M is N // 2 ; M is (3 * N) + 1 ), sequence(M). sequence_length(Start, Length) :- integer(Start), Start >= 1, sequence_length(Start, 1, Length). sequence_length(1, Length, Length) :- !. sequence_length(N, Length0, Length) :- Length1 is Length0 + 1, ( N mod 2 =:= 0 -> M is N // 2 ; M is (3 * N) + 1 ), sequence_length(M, Length1, Length). longest_sequence(Start, End, N, Length) :- integer(Start), integer(End), Start >= 1, Start =< End, longest_sequence(Start, End, 1, N, 1, Length). longest_sequence(Current, End, N, N, Length, Length) :- Current > End, !. longest_sequence(Current, End, N0, N, Length0, Length) :- sequence_length(Current, 1, CurrentLength), Next is Current + 1, ( CurrentLength > Length0 -> longest_sequence(Next, End, Current, N, CurrentLength, Length) ; longest_sequence(Next, End, N0, N, Length0, Length) ). :- end_object. Testing: | ?- hailstone::write_sequence(27).27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1true | ?- hailstone::sequence_length(27, Length).Length = 112true | ?- hailstone::longest_sequence(1, 100000, N, Length).N = 77031, Length = 351true ## LOLCODE There is presently no way to query a BUKKIT for the existence of a given key, thus making memoization infeasible. This solution takes advantage of prior knowledge to run in reasonable time. HAI 1.3 HOW IZ I hailin YR stone I HAS A sequence ITZ A BUKKIT sequence HAS A length ITZ 1 sequence HAS A SRS 0 ITZ stone IM IN YR stoner BOTH SAEM stone AN 1, O RLY? YA RLY, FOUND YR sequence OIC MOD OF stone AN 2, O RLY? YA RLY, stone R SUM OF PRODUKT OF stone AN 3 AN 1 NO WAI, stone R QUOSHUNT OF stone AN 2 OIC sequence HAS A SRS sequence'Z length ITZ stone sequence'Z length R SUM OF sequence'Z length AN 1 IM OUTTA YR stonerIF U SAY SO I HAS A hail27 ITZ I IZ hailin YR 27 MKAYVISIBLE "hail(27) = "! IM IN YR first4 UPPIN YR i TIL BOTH SAEM i AN 4 VISIBLE hail27'Z SRS i " "!IM OUTTA YR first4VISIBLE "..."! IM IN YR last4 UPPIN YR i TIL BOTH SAEM i AN 4 VISIBLE " " hail27'Z SRS SUM OF 108 AN i!IM OUTTA YR last4VISIBLE ", length = " hail27'Z length I HAS A max, I HAS A len ITZ 0 BTW, DIS IZ RLY NOT FAST SO WE ONLY CHEK N IN [75000, 80000)IM IN YR maxer UPPIN YR n TIL BOTH SAEM n AN 5000 I HAS A n ITZ SUM OF n AN 75000 I HAS A seq ITZ I IZ hailin YR n MKAY BOTH SAEM len AN SMALLR OF len AN seq'Z length, O RLY? YA RLY, max R n, len R seq'Z length OICIM OUTTA YR maxer VISIBLE "len(hail(" max ")) = " len KTHXBYE Output: hail(27) = 27 82 41 124 ... 8 4 2 1, length = 112 len(hail(77031)) = 351 ## Lua function hailstone( n, print_numbers ) local n_iter = 1 while n ~= 1 do if print_numbers then print( n ) end if n % 2 == 0 then n = n / 2 else n = 3 * n + 1 end n_iter = n_iter + 1 end if print_numbers then print( n ) end return n_iter;end hailstone( 27, true ) max_i, max_iter = 0, 0for i = 1, 100000 do num = hailstone( i, false ) if num >= max_iter then max_i = i max_iter = num endend print( string.format( "Needed %d iterations for the number %d.\n", max_iter, max_i ) ) ## M2000 Interpreter Use of two versions of Hailstone, one which return each n, and another one which return only the length of sequence. Also we use current stack as FIFO to get the last 4 numbers  Module hailstone.Task { hailstone=lambda (n as long)->{ =lambda n (&val) ->{ if n=1 then =false: exit =true if n mod 2=0 then n/=2 : val=n: exit n*=3 : n++: val=n } } Count=Lambda (n) ->{ m=lambda n ->{ if n=1 then =false: exit =true :if n mod 2=0 then n/=2 :exit n*=3 : n++ } c=1 While m() {c++} =c } k=Hailstone(27) counter=1 x=0 Print 27, While k(&x) { counter++ Print x, if counter=4 then exit } Print Flush ' empty current stack While k(&x) { counter++ data x ' send to end of stack -used as FIFO if stack.size>4 then drop } \\ [] return a stack object and leave empty current stack \\ Print use automatic iterator to print all values in columns. Print [] Print "counter:";counter m=0 For i=2 to 99999 { m1=max.data(count(i), m) if m1<>m then m=m1: im=i } Print Format("Number {0} has then longest hailstone sequence of length {1}", im, m)}hailstone.Task  Output:  27 82 41 124 8 4 2 1 counter:112 Number 77031 has then longest hailstone sequence of length 351  ## Maple Define the procedure:  hailstone := proc( N ) local n := N, HS := Array([n]); while n > 1 do if type(n,even) then n := n/2; else n := 3*n+1; end if; HS(numelems(HS)+1) := n; end do; HS;end proc;  Run the command and show the appropriate portion of the result;  > r := hailstone(27): [ 1..112 1-D Array ] r := [ Data Type: anything ] [ Storage: rectangular ] [ Order: Fortran_order ]> r(1..4) ... r(-4..); [27, 82, 41, 124] .. [8, 4, 2, 1]  Compute the first 100000 sequences:  longest := 0; n := 0;for i from 1 to 100000 do len := numelems(hailstone(i)); if len > longest then longest := len; n := i; end if;od:printf("The longest Hailstone sequence in the first 100k is n=%d, with %d terms\n",n,longest);  Output: The longest Hailstone sequence in the first 100k is n=77031, with 351 terms  ## Mathematica / Wolfram Language Here are four ways to generate the sequence. ### Nested function call formulation HailstoneF[n_] := NestWhileList[If[[email protected]#, 3 # + 1, #/2] &, n, # > 1 &] This is probably the most readable and shortest implementation. ### Fixed-Point formulation HailstoneFP[n_] := [email protected][Switch[#, 1, 1, _?OddQ , 3# + 1, _, #/2] &, n] ### Recursive formulation HailstoneR[1] = {1}HailstoneR[n_?OddQ] := Prepend[HailstoneR[3 n + 1], n]HailstoneR[n_] := Prepend[HailstoneR[n/2], n]  ### Procedural implementation HailstoneP[n_] := Module[{x = {n}, s = n}, While[s > 1, x = {x, s = If[[email protected], 3 s + 1, s/2]}]; [email protected]]  ### Validation I use this version to do the validation: Hailstone[n_] := NestWhileList[Which[Mod[#, 2] == 0, #/2, True, ( 3*# + 1) ] &, n, # != 1 &]; c27 = [email protected];Print["Hailstone sequence for n = 27: [", c27[[;; 4]], "...", c27[[-4 ;;]], "]"]Print["Length Hailstone[27] = ", [email protected]] longest = -1; comp = 0;Do[temp = [email protected]@i; If[comp < temp, comp = temp; longest = i], {i, 100000} ]Print["Longest Hailstone sequence at n = ", longest, "\nwith length = ", comp];  Output: Hailstone sequence for n = 27: [{27,82,41,124}...{8,4,2,1}] Length Hailstone[27] = 112 Longest Hailstone sequence at n = 77031 with length = 351  I think the fixed-point and the recursive piece-wise function formulations are more idiomatic for Mathematica #### Sequence 27 With[{seq = HailstoneFP[27]}, { Length[seq], Take[seq, 4], Take[seq, -4]}] Output: {112, {27, 82, 41, 124}, {8, 4, 2, 1}} Alternatively, Short[HailstoneFP[27],0.45] Output: {27, 82, 41, 124, <<104>>, 8, 4, 2, 1} #### Longest sequence length MaximalBy[Table[{i, Length[HailstoneFP[i]]}, {i, 100000}], Last] Output: {{77031, 351}} ## MATLAB / Octave ### Hailstone Sequence For N function x = hailstone(n) x = n; while n > 1 % faster than mod(n, 2) if n ~= floor(n / 2) * 2 n = n * 3 + 1; else n = n / 2; end x(end + 1) = n; %#ok end Show sequence of hailstone(27) and number of elements: x = hailstone(27);fprintf('hailstone(27): %d %d %d %d ... %d %d %d %d\nnumber of elements: %d\n', x(1:4), x(end-3:end), numel(x)) Output: hailstone(27): 27 82 41 124 ... 8 4 2 1 number of elements: 112 ### Longest Hailstone Sequence Under N Show the number less than 100,000 which has the longest hailstone sequence together with that sequence's length: #### Basic Version (use the above routine) N = 1e5;maxLen = 0;for k = 1:N kLen = numel(hailstone(k)); if kLen > maxLen maxLen = kLen; n = k; endend Output: n = 77031 maxLen = 351 #### Faster Version function [n, maxLen] = longestHailstone(N) maxLen = 0; for k = 1:N a = k; kLen = 1; while a > 1 if a ~= floor(a / 2) * 2 a = a * 3 + 1; else a = a / 2; end kLen = kLen + 1; end if kLen > maxLen maxLen = kLen; n = k; end end Output: >> [n, maxLen] = longestHailstone(1e5)n = 77031maxLen = 351 #### Much Faster Version With Caching function [n, maxLen] = longestHailstone(N) lenList(N) = 0; lenList(1) = 1; maxLen = 0; for k = 2:N a = k; kLen = 0; while a >= k if a == floor(a / 2) * 2 a = a / 2; else a = a * 3 + 1; end kLen = kLen + 1; end kLen = kLen + lenList(a); lenList(k) = kLen; if kLen > maxLen maxLen = kLen; n = k; end end Output: >> [n, maxLen] = longestHailstone(1e5)n = 77031maxLen = 351 ## Maxima collatz(n) := block([L], L: [n], while n > 1 do(n: if evenp(n) then n/2 else 3*n + 1, L: endcons(n, L)), L) collatz_length(n) := block([m], m: 1, while n > 1 do(n: if evenp(n) then n/2 else 3*n + 1, m: m + 1), m) collatz_max(n) := block([j, m, p], m: 0,for i from 1 thru n do (p: collatz_length(i), if p > m then (m: p, j: i)),[j, m]) collatz(27); /* [27, 82, 41, ..., 4, 2, 1] */length(%); /* 112 */collatz_length(27); /* 112 */collatz_max(100000); /* [77031, 351] */ ## Mercury The actual calculation (including module ceremony) providing both a function and a predicate implementation: :- module hailstone. :- interface. :- import_module int, list. :- func hailstone(int) = list(int).:- pred hailstone(int::in, list(int)::out) is det. :- implementation. hailstone(N) = S :- hailstone(N, S). hailstone(N, [N|S]) :- ( N = 1 -> S = [] ; N mod 2 = 0 -> hailstone(N/2, S) ; hailstone(3 * N + 1, S) ). :- end_module hailstone. The mainline test driver (making use of unification for more succinct tests): :- module test_hailstone. :- interface. :- import_module io. :- pred main(io.state::di, io.state::uo) is det. :- implementation. :- import_module int, list.:- import_module hailstone. :- pred longest(int::in, int::out, int::out) is det.:- pred longest(int::in, int::in, int::in, int::out, int::out) is det. longest(M, N, L) :- longest(M, 0, 0, N, L). longest(N, CN, CL, MN, ML) :- ( N > 1 -> L = list.length(hailstone(N)), ( L > CL -> longest(N - 1, N, L, MN, ML) ; longest(N - 1, CN, CL, MN, ML) ) ; MN = CN, ML = CL ). main(!IO) :- S = hailstone(27), ( list.length(S) = 112, list.append([27, 82, 41, 124], _, S), list.remove_suffix(S, [8, 4, 2, 1], _), longest(100000, 77031, 351) -> io.write_string("All tests succeeded.\n", !IO) ; io.write_string("At least one test failed.\n", !IO) ). :- end_module test_hailstone. Output: of running this program is: All tests succeeded.  For those unused to logic programming languages it seems that nothing has been proved in terms of confirming anything, but if you look at the predicate declaration for longest/3 :- pred longest(int::in, int::out, int::out) is det. … you see that the second and third parameters are output parameters. This by calling longest(100000, 77031, 351) you prove, through unification, that the longest sequence is with the number 77031 and that it is 351 cycles long. Similarly, using list.append([27, 82, 41, 124], _, S) automatically proves that the generated sequence begins with the provided sequence, etc. Thus we know that the correct sequences and values were generated without bothering to print them out. ## ML ### MLite fun hail (x = 1) = [1] | (x rem 2 = 0) = x :: hail (x div 2) | x = x :: hail (x * 3 + 1) fun hailstorm ([], i, largest, largest_at) = (largest_at, largest) | (x :: xs, i, largest, largest_at) = let val k = len (hail x) in if k > largest then hailstorm (xs, i + 1, k, i) else hailstorm (xs, i + 1, largest, largest_at) end | (x :: xs) = hailstorm (x :: xs, 1, 0, 0) ; val h27 = hail 27;print "hailstone sequence for the number 27 has ";print  len (h27);print " elements starting with ";print  sub (h27, 0, 4);print " and ending with ";print  sub (h27, len(h27)-4, len h27);println "."; val biggest = hailstorm  iota (100000 - 1); print "The number less than 100,000 which has the longest ";print "hailstone sequence is at element ";print  ref (biggest, 0);print " and is of length ";println  ref (biggest, 1); Output: hailstone sequence for the number 27 has 112 elements starting with [27, 82, 41, 124] and ending with [8, 4, 2, 1]. The number less than 100,000 which has the longest hailstone sequence is at element 77031 and is of length 351 ## Modula-2 MODULE hailst; IMPORT InOut; CONST maxCard = MAX (CARDINAL) DIV 3;TYPE action = (List, Count, Max);VAR a : CARDINAL; PROCEDURE HailStone (start : CARDINAL; type : action) : CARDINAL; VAR n, max, count : CARDINAL; BEGIN count := 1; n := start; max := n; LOOP IF type = List THEN InOut.WriteCard (n, 12); IF count MOD 6 = 0 THEN InOut.WriteLn END END; IF n = 1 THEN EXIT END; IF ODD (n) THEN IF n < maxCard THEN n := 3 * n + 1; IF n > max THEN max := n END ELSE InOut.WriteString ("Exceeding max value for type CARDINAL at count = "); InOut.WriteCard (count, 10); InOut.WriteString (" for intermediate value "); InOut.WriteCard (n, 10); InOut.WriteString (". Aborting."); HALT END ELSE n := n DIV 2 END; INC (count) END; IF type = Max THEN RETURN max ELSE RETURN count ENDEND HailStone; PROCEDURE FindMax (num : CARDINAL); VAR val, maxCount, maxVal, cnt : CARDINAL; BEGIN maxCount := 0; maxVal := 0; FOR val := 2 TO num DO cnt := HailStone (val, Count); IF cnt > maxCount THEN maxVal := val; maxCount := cnt END END; InOut.WriteString ("Longest sequence below "); InOut.WriteCard (num, 1); InOut.WriteString (" is "); InOut.WriteCard (HailStone (maxVal, Count), 1); InOut.WriteString (" for n = "); InOut.WriteCard (maxVal, 1); InOut.WriteString (" with an intermediate maximum of "); InOut.WriteCard (HailStone (maxVal, Max), 1); InOut.WriteLnEND FindMax; BEGIN a := HailStone (27, List); InOut.WriteLn; InOut.WriteString ("Iterations total = "); InOut.WriteCard (HailStone (27, Count), 12); InOut.WriteString (" max value = "); InOut.WriteCard (HailStone (27, Max) , 12); InOut.WriteLn; FindMax (100000); InOut.WriteString ("Done."); InOut.WriteLnEND hailst. Producing: [email protected]:~/modula/rosetta hailst 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Iterations total = 112 max value = 9232 Longest sequence below 100000 is 351 for n = 77031 with an intermediate maximum of 21933016 Done. When trying the same for all values below 1 million: Exceeding max value for type CARDINAL at n = 159487 , count = 60 and intermediate value 1699000271. Aborting. ## MUMPS hailstone(n) ; If n=1 Quit n If n#2 Quit n_" "_$$hailstone(3*n+1)	Quit n_" "_$$hailstone(n\2)Set x=$$hailstone(27) Write !,$Length(x," ")," terms in ",x,!112 terms in 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 ## NetRexx /* NetRexx */ options replace format comments java crossref savelog symbols binary do start = 27 hs = hailstone(start) hsCount = hs.words say 'The number' start 'has a hailstone sequence comprising' hsCount 'elements' say ' its first four elements are:' hs.subword(1, 4) say ' and last four elements are:' hs.subword(hsCount - 3) hsMax = 0 hsCountMax = 0 llimit = 100000 loop x_ = 1 to llimit - 1 hs = hailstone(x_) hsCount = hs.words if hsCount > hsCountMax then do hsMax = x_ hsCountMax = hsCount end end x_ say 'The number' hsMax 'has the longest hailstone sequence in the range 1 to' llimit - 1 'with a sequence length of' hsCountMaxcatch ex = Exception ex.printStackTraceend return method hailstone(hn = long) public static returns Rexx signals IllegalArgumentException hs = Rexx('') if hn <= 0 then signal IllegalArgumentException('Invalid start point. Must be a positive integer greater than 0') loop label n_ while hn > 1 hs = hs' 'hn if hn // 2 \= 0 then hn = hn * 3 + 1 else hn = hn % 2 end n_ hs = hs' 'hn return hs.strip Output: The number 27 has a hailstone sequence comprising 112 elements its first four elements are: 27 82 41 124 and last four elements are: 8 4 2 1 The number 77031 has the longest hailstone sequence in the range 1 to 99999 with a sequence length of 351  ## Nim Translation of: Python proc hailstone(n): auto = result = @[n] var n = n while n > 1: if (n and 1) == 1: n = 3 * n + 1 else: n = n div 2 result.add n let h = hailstone 27assert h.len == 112 and h[0..3] == @[27,82,41,124] and h[h.high-3..h.high] == @[8,4,2,1]var m, mi = 0for i in 1 .. <100_000: let n = hailstone(i).len if n > m: m = n mi = iecho "Maximum length ", m, " was found for hailstone(", mi, ") for numbers <100,000" Output: Maximum length 351 was found for hailstone(77031) for numbers <100,000 ## Oberon-2 MODULE hailst; IMPORT Out; CONST maxCard = MAX (INTEGER) DIV 3; List = 1; Count = 2; Max = 3; VAR a : INTEGER; PROCEDURE HailStone (start, type : INTEGER) : INTEGER; VAR n, max, count : INTEGER; BEGIN count := 1; n := start; max := n; LOOP IF type = List THEN Out.Int (n, 12); IF count MOD 6 = 0 THEN Out.Ln END END; IF n = 1 THEN EXIT END; IF ODD (n) THEN IF n < maxCard THEN n := 3 * n + 1; IF n > max THEN max := n END ELSE Out.String ("Exceeding max value for type INTEGER at: "); Out.String (" n = "); Out.Int (start, 12); Out.String (" , count = "); Out.Int (count, 12); Out.String (" and intermediate value "); Out.Int (n, 1); Out.String (". Aborting."); Out.Ln; HALT (2) END ELSE n := n DIV 2 END; INC (count) END; IF type = Max THEN RETURN max ELSE RETURN count ENDEND HailStone; PROCEDURE FindMax (num : INTEGER); VAR val, maxCount, maxVal, cnt : INTEGER; BEGIN maxCount := 0; maxVal := 0; FOR val := 2 TO num DO cnt := HailStone (val, Count); IF cnt > maxCount THEN maxVal := val; maxCount := cnt END END; Out.String ("Longest sequence below "); Out.Int (num, 1); Out.String (" is "); Out.Int (HailStone (maxVal, Count), 1); Out.String (" for n = "); Out.Int (maxVal, 1); Out.String (" with an intermediate maximum of "); Out.Int (HailStone (maxVal, Max), 1); Out.LnEND FindMax; BEGIN a := HailStone (27, List); Out.Ln; Out.String ("Iterations total = "); Out.Int (HailStone (27, Count), 12); Out.String (" max value = "); Out.Int (HailStone (27, Max) , 12); Out.Ln; FindMax (1000000); Out.String ("Done."); Out.LnEND hailst. Producing  27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Iterations total = 112 max value = 9232 Exceeding max value for type INTEGER at: n = 113383 , count = 120 and intermediate value 827370449. Aborting. ## OCaml #load "nums.cma";;open Num;; (* generate Hailstone sequence *)let hailstone n = let one = Int 1 and two = Int 2 and three = Int 3 in let rec g s x = if x =/ one then x::s else g (x::s) (if mod_num x two =/ one then three */ x +/ one else x // two) in g [] (Int n);; (* compute only sequence length *)let haillen n = let one = Int 1 and two = Int 2 and three = Int 3 in let rec g s x = if x =/ one then s+1 else g (s+1) (if mod_num x two =/ one then three */ x +/ one else x // two) in g 0 (Int n);; (* max length for starting values in 1..n *)let hailmax = let rec g idx len = function | 0 -> (idx, len) | i -> let a = haillen i in if a > len then g i a (i-1) else g idx len (i-1) in g 0 0;; hailmax 100000 ;;(* - : int * int = (77031, 351) *) List.rev_map string_of_num (hailstone 27) ;; (* - : string list =["27"; "82"; "41"; "124"; "62"; "31"; "94"; "47"; "142"; "71"; "214"; "107"; "322"; "161"; "484"; "242"; "121"; "364"; "182"; "91"; "274"; "137"; "412"; "206"; "103"; "310"; "155"; "466"; "233"; "700"; "350"; "175"; "526"; "263"; "790"; "395"; "1186"; "593"; "1780"; "890"; "445"; "1336"; "668"; "334"; "167"; "502"; "251"; "754"; "377"; "1132"; "566"; "283"; "850"; "425"; "1276"; "638"; "319"; "958"; "479"; "1438"; "719"; "2158"; "1079"; "3238"; "1619"; "4858"; "2429"; "7288"; "3644"; "1822"; "911"; "2734"; "1367"; "4102"; "2051"; "6154"; "3077"; "9232"; "4616"; "2308"; "1154"; "577"; "1732"; "866"; "433"; "1300"; "650"; "325"; "976"; "488"; "244"; "122"; "61"; "184"; "92"; "46"; "23"; "70"; "35"; "106"; "53"; "160"; "80"; "40"; "20"; "10"; "5"; "16"; "8"; "4"; "2"; "1"] *) ## Oforth : hailstone // n -- [n]| l | ListBuffer new ->l while(dup 1 <>) [ dup l add dup isEven ifTrue: [ 2 / ] else: [ 3 * 1+ ] ] l add l dup freeze ; hailstone(27) dup size println dup left(4) println right(4) println100000 seq map(#[ dup hailstone size swap Pair new ]) reduce(#maxKey) println Output: 112 [27, 82, 41, 124] [8, 4, 2, 1] [351, 77031]  ## ooRexx  sequence = hailstone(27)say "Hailstone sequence for 27 has" sequence~items "elements and is ["sequence~toString('l', ", ")"]" highestNumber = 1highestCount = 1 loop i = 2 to 100000 sequence = hailstone(i) count = sequence~items if count > highestCount then do highestNumber = i highestCount = count endendsay "Number" highestNumber "has the longest sequence with" highestCount "elements" -- short routine to generate a hailstone sequence::routine hailstone use arg n sequence = .array~of(n) loop while n \= 1 if n // 2 == 0 then n = n / 2 else n = 3 * n + 1 sequence~append(n) end return sequence  Output: Hailstone sequence for 27 has 112 elements and is [27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 77, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 102, 051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 0, 40, 20, 10, 5, 16, 8, 4, 2, 1] Number 77031 has the longest sequence with 351 elements  ## Order To display the length, and first and last elements, of the hailstone sequence for 27, we could do this: #include <order/interpreter.h> #define ORDER_PP_DEF_8hailstone ORDER_PP_FN( \8fn(8N, \ 8cond((8equal(8N, 1), 8seq(1)) \ (8is_0(8remainder(8N, 2)), \ 8seq_push_front(8N, 8hailstone(8quotient(8N, 2)))) \ (8else, \ 8seq_push_front(8N, 8hailstone(8inc(8times(8N, 3))))))) ) ORDER_PP( 8lets((8H, 8seq_map(8to_lit, 8hailstone(27))) (8S, 8seq_size(8H)), 8print(8(h(27) - length:) 8to_lit(8S) 8comma 8space 8(starts with:) 8seq_take(4, 8H) 8comma 8space 8(ends with:) 8seq_drop(8minus(8S, 4), 8H)) ) ) Output: h(27) - length:112, starts with:(27)(82)(41)(124), ends with:(8)(4)(2)(1) Unfortunately, the C preprocessor not really being designed with large amounts of garbage collection in mind, trying to compute the hailstone sequences up to 100000 is almost guaranteed to run out of memory (and take a very, very long time). If we wanted to try, we could add this to the program, which in most languages would use relatively little memory: #define ORDER_PP_DEF_8h_longest ORDER_PP_FN( \8fn(8M, 8P, \ 8if(8is_0(8M), \ 8P, \ 8let((8L, 8seq_size(8hailstone(8M))), \ 8h_longest(8dec(8M), \ 8if(8greater(8L, 8tuple_at_1(8P)), \ 8pair(8M, 8L), 8P))))) ) ORDER_PP( 8let((8P, 8h_longest(8nat(1,0,0,0,0,0), 8pair(0, 0))), 8pair(8to_lit(8tuple_at_0(8P)), 8to_lit(8tuple_at_1(8P))))) ...or even this "more elegant" version, which will run out of memory very quickly indeed (but in practice seems to work better for smaller ranges): ORDER_PP( 8let((8P, 8seq_head( 8seq_sort(8fn(8P, 8Q, 8greater(8tuple_at_1(8P), 8tuple_at_1(8Q))), 8seq_map(8fn(8N, 8pair(8N, 8seq_size(8hailstone(8N)))), 8seq_iota(1, 8nat(1,0,0,0,0,0)))))), 8pair(8to_lit(8tuple_at_0(8P)), 8to_lit(8tuple_at_1(8P)))) ) Notice that large numbers (>100) must be entered as digit sequences with 8nat. 8to_lit converts a digit sequence back to a readable number. ## Oz declare fun {HailstoneSeq N} N > 0 = true %% assert if N == 1 then [1] elseif {IsEven N} then N|{HailstoneSeq N div 2} else N|{HailstoneSeq 3*N+1} end end HSeq27 = {HailstoneSeq 27} {Length HSeq27} = 112 {List.take HSeq27 4} = [27 82 41 124] {List.drop HSeq27 108} = [8 4 2 1] fun {MaxBy2nd A=A1#A2 B=B1#B2} if B2 > A2 then B else A end end Pairs = {Map {List.number 1 99999 1} fun {$ I} I#{Length {HailstoneSeq I}} end}   MaxI#MaxLen = {List.foldL Pairs MaxBy2nd 0#0}  {System.showInfo   "Maximum length "#MaxLen#" was found for hailstone("#MaxI#")"}
Output:
Maximum length 351 was found for hailstone(77031)


## PARI/GP

### Version #1.

show(n)={  my(t=1);  while(n>1,    print1(n",");    n=if(n%2,      3*n+1    ,      n/2    );    t++  );  print(1);  t}; len(n)={  my(t=1);  while(n>1,    if(n%2,      t+=2;      n+=(n>>1)+1    ,      t++;      n>>=1    )  );  t}; show(27)r=0;for(n=1,1e5,t=len(n);if(t>r,r=t;ra=n));print(ra"\t"r)
Output:
27,82,41,124,62,31,94,47,142,71,214,107,322,161,484,242,121,364,182,91,274,137,4
12,206,103,310,155,466,233,700,350,175,526,263,790,395,1186,593,1780,890,445,133
6,668,334,167,502,251,754,377,1132,566,283,850,425,1276,638,319,958,479,1438,719
,2158,1079,3238,1619,4858,2429,7288,3644,1822,911,2734,1367,4102,2051,6154,3077,
9232,4616,2308,1154,577,1732,866,433,1300,650,325,976,488,244,122,61,184,92,46,2
3,70,35,106,53,160,80,40,20,10,5,16,8,4,2,1

and

77031   351

### Version #2.

Works with: PARI/GP version 2.7.4 and above

Different kind of PARI scripts for Collatz sequences you can find in OEIS, e.g.: A070165

 \\ Get vector with Collatz sequence for the specified starting number.\\ Limit vector to the lim length, or less, if 1 (one) term is reached (when lim=0).\\ 3/26/2016 aevCollatz(n,lim=0)={my(c=n,e=0,L=List(n)); if(lim==0, e=1; lim=n*10^6); for(i=1,lim, if(c%2==0, c=c/2, c=3*c+1); listput(L,c); if(e&&c==1, break));return(Vec(L)); } Collatzmax(ns,nf)={my(V,vn,mxn=1,mx,im=1);print("Search range: ",ns,"..",nf);for(i=ns,nf, V=Collatz(i); vn=#V; if(vn>mxn, mxn=vn; im=i); kill(V)); print("Hailstone/Collatz(",im,") has the longest length = ",mxn);}  {\\ Required tests:print("Required tests:");my(Vr,vrn);Vr=Collatz(27); vrn=#Vr;print("Hailstone/Collatz(27): ",Vr[1..4]," ... ",Vr[vrn-3..vrn],"; length = ",vrn);Collatzmax(1,100000);}
Output:
Required tests:
Hailstone/Collatz(27): [27, 82, 41, 124] ... [8, 4, 2, 1]; length = 112
Search range: 1..100000
Hailstone/Collatz(77031) has the longest length = 351

(15:32) gp > ##
***   last result computed in 15,735 ms.


## Pascal

See Delphi or try this transformed Delphi version without generics.Use of a static array.

program ShowHailstoneSequence;{$IFDEF FPC} {$MODE delphi} //or objfpc{$Else} {$Apptype Console} // for delphi{$ENDIF}uses SysUtils;// formatconst maxN = 10*1000*1000;// for output 1000*1000*1000 type tiaArr = array[0..1000] of Uint64; tIntArr = record iaMaxPos : integer; iaArr : tiaArr end; tpiaArr = ^tiaArr; function HailstoneSeqCnt(n: UInt64): NativeInt;begin result := 0; //ensure n to be odd while not(ODD(n)) do Begin inc(result); n := n shr 1; end; IF n > 1 then repeat //now n == odd -> so two steps in one can be made repeat n := (3*n+1) SHR 1;inc(result,2); until NOT(Odd(n)); //now n == even -> so only one step can be made repeat n := n shr 1; inc(result); until odd(n); until n = 1;end; procedure GetHailstoneSequence(aStartingNumber: NativeUint;var aHailstoneList: tIntArr);var maxPos: NativeInt; n: UInt64; pArr : tpiaArr;begin with aHailstoneList do begin maxPos := 0; pArr := @iaArr; end; n := aStartingNumber; pArr^[maxPos] := n; while n <> 1 do begin if odd(n) then n := (3*n+1) else n := n shr 1; inc(maxPos); pArr^[maxPos] := n; end; aHailstoneList.iaMaxPos := maxPos;end; var i,Limit: NativeInt; lList: tIntArr; lAverageLength:Uint64; lMaxSequence: NativeInt; lMaxLength,lgth: NativeInt;begin lList.iaMaxPos := 0; GetHailstoneSequence(27, lList);//319804831 with lList do begin Limit := iaMaxPos; writeln(Format('sequence of %d has %d elements',[iaArr[0],Limit+1])); write(iaArr[0],',',iaArr[1],',',iaArr[2],',',iaArr[3],'..'); For i := iaMaxPos-3 to iaMaxPos-1 do write(iaArr[i],','); writeln(iaArr[iaMaxPos]); end; Writeln; lMaxSequence := 0; lMaxLength := 0; i := 1; limit := 10*i; writeln(' Limit : number with max length | average length'); repeat lAverageLength:= 0; repeat lgth:= HailstoneSeqCnt(i); inc(lAverageLength, lgth); if lgth >= lMaxLength then begin lMaxSequence := i; lMaxLength := lgth+1; end; inc(i); until i = Limit; Writeln(Format(' %10d : %9d | %4d | %7.3f', [limit,lMaxSequence, lMaxLength,0.9*lAverageLength/Limit])); limit := limit*10; until Limit > maxN;end. Output: sequence of 27 has 112 elements 27,82,41,124..8,4,2,1 Limit : number with max length | average length 10 : 9 | 20 | 5.490 100 : 97 | 119 | 27.504 1000 : 871 | 179 | 50.683 10000 : 6171 | 262 | 71.119 100000 : 77031 | 351 | 89.137 1000000 : 837799 | 525 | 108.613 10000000 : 8400511 | 686 | 127.916 100000000 : 63728127 | 950 | 147.337 1000000000 : 670617279 | 987 | 166.780 real 6m22.968s // 32-bit compiled real 3m56.573s // 64-bit compiled ## Perl ### Straightforward #!/usr/bin/perl use warnings;use strict; my @h = hailstone(27);print "Length of hailstone(27) = " . scalar @h . "\n";print "[" . join(", ", @h[0 .. 3], "...", @h[-4 .. -1]) . "]\n"; my ($max, $n) = (0, 0);for my$x (1 .. 99_999) {    @h = hailstone($x); if (scalar @h >$max) {        ($max,$n) = (scalar @h, $x); }} print "Max length$max was found for hailstone($n) for numbers < 100_000\n"; sub hailstone { my ($n) = @_;     my @sequence = ($n); while ($n > 1) {        if ($n % 2 == 0) {$n = int($n / 2); } else {$n = $n * 3 + 1; } push @sequence,$n;    }     return @sequence;}
Output:
Length of hailstone(27) = 112
[27, 82, 41, 124, ..., 8, 4, 2, 1]
Max length 351 was found for hailstone(77031) for numbers < 100_000


### Compact

A more compact version:

#!/usr/bin/perluse strict; sub hailstone {    @_ = local $_ = shift; push @_,$_ = $_ % 2 ? 3 *$_ + 1 : $_ / 2 while$_ > 1;    @_;} my @h = hailstone($_ = 27);print "$_: @h[0 .. 3] ... @h[-4 .. -1] (".@h.")\n"; @h = ();for (1 .. 99_999) { @h = ($_,$h[2]) if ($h[2] = hailstone($_)) > $h[1] }printf "%d: (%d)\n", @h; Output: 27: 27 82 41 124 ... 8 4 2 1 (112) 77031: (351)  ## Perl 6 sub hailstone($n) { $n, {$_ %% 2 ?? $_ div 2 !!$_ * 3 + 1 } ... 1 } my @h = hailstone(27);say "Length of hailstone(27) = {[email protected]}";say ~@h; my $m = max ( (1..99_999).race.map: { +hailstone($_) => $_ } );say "Max length {$m.key} was found for hailstone({$m.value}) for numbers < 100_000"; Output: Length of hailstone(27) = 112 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1 Max length 351 was found for hailstone(77031) for numbers < 100_000  ## Phix Copy of Euphoria function hailstone(atom n)sequence s = {n} while n!=1 do if remainder(n,2)=0 then n /= 2 else n = 3*n+1 end if s &= n end while return send function function hailstone_count(atom n)integer count = 1 while n!=1 do if remainder(n,2)=0 then n /= 2 else n = 3*n+1 end if count += 1 end while return countend function sequence s = hailstone(27)integer ls = length(s)s[5..-5] = {".."}puts(1,"hailstone(27) = ")? sprintf(1,"length = %d\n\n",ls) integer hmax = 1, imax = 1,countfor i=2 to 1e5-1 do count = hailstone_count(i) if count>hmax then hmax = count imax = i end ifend for printf(1,"The longest hailstone sequence under 100,000 is %d with %d elements.\n",{imax,hmax}) Output: hailstone(27) = {27,82,41,124,"..",8,4,2,1} length = 112 The longest hailstone sequence under 100,000 is 77031 with 351 elements.  ## PHP function hailstone($n,$seq=array()){$sequence = $seq;$sequence[] = $n; if($n == 1){		return $sequence; }else{$n = ($n%2==0) ?$n/2 : (3*$n)+1; return hailstone($n, $sequence); }}$result = hailstone(27);echo count($result) . ' Elements.<br>';echo 'Starting with : ' . implode(",",array_slice($result,0,4)) .' and ending with : ' . implode(",",array_slice($result,count($result)-4)) . '<br>'; $maxResult = array(0); for($i=1;$i<=100000;$i++){		$result = count(hailstone($i));		if($result > max($maxResult)){			$maxResult = array($i=>$result); }}foreach($maxResult as $key =>$val){echo 'Number < 100000 with longest Hailstone seq.: ' . $key . ' with length of ' .$val;}
112 Elements.
Starting with : 27,82,41,124 and ending with : 8,4,2,1
Number < 100000 with longest Hailstone seq.: 77031 with length of 351


## PicoLisp

(de hailstone (N)   (make      (until (= 1 (link N))         (setq N            (if (bit? 1 N)               (inc (* N 3))               (/ N 2) ) ) ) ) ) (let L (hailstone 27)   (println 27 (length L) (head 4 L) '- (tail 4 L)) ) (let N (maxi '((N) (length (hailstone N))) (range 1 100000))   (println N (length (hailstone N))) )
Output:
27 112 (27 82 41 124) - (8 4 2 1)
77031 351

## Pike

#!/usr/bin/env pike int next(int n){    if (n==1)        return 0;    if (n%2)        return 3*n+1;    else        return n/2;} array(int) hailstone(int n){    array seq = ({ n });    while (n=next(n))        seq += ({ n });    return seq;} void main(){    array(int) two = hailstone(27);    if (equal(two[0..3], ({ 27, 82, 41, 124 })) && equal(two[<3..], ({ 8,4,2,1 })))        write("sizeof(({ %{%d, %}, ... %{%d, %} }) == %d\n", two[0..3], two[<3..], sizeof(two));     mapping longest = ([ "length":0, "start":0 ]);     foreach(allocate(100000); int start; )    {        int length = sizeof(hailstone(start));        if (length > longest->length)        {            longest->length = length;            longest->start = start;        }    }    write("longest sequence starting at %d has %d elements\n", longest->start, longest->length);}
Output:
 sizeof(({ 27, 82, 41, 124, , ... 8, 4, 2, 1,  }) == 112
longest sequence starting at 77031 has 351 elements


## PL/I

test: proc options (main);   declare (longest, n) fixed (15);   declare flag bit (1);   declare (i, value) fixed (15);    /* Task 1: */   flag = '1'b;   put skip list ('The sequence for 27 is');   i = hailstones(27);    /* Task 2: */   flag = '0'b;   longest = 0;   do i = 1 to 99999;      if longest < hailstones(i) then         do; longest = hailstones(i); value = i; end;   end;   put skip edit (value, ' has the longest sequence of ', longest) (a); hailstones: procedure (n) returns ( fixed (15));   declare n fixed (15) nonassignable;   declare (m, p) fixed (15);    m = n;   p = 1;   if flag then put skip list (m);   do p = 1 by 1 while (m > 1);      if iand(m, 1) = 0 then         m = m/2;      else         m = 3*m + 1;      if flag then put skip list (m);   end;   if flag then put skip list ('The hailstone sequence has length' || p);   return (p);end hailstones; end test;
Output:
The sequence for 27 is
27
82
41
124
62
31
94
47
142
71
214
107
322
161
484
242
121
364
182
91
274
137
412
206
103
310
155
466
233
700
350
175
526
263
790
395
1186
593
1780
890
445
1336
668
334
167
502
251
754
377
1132
566
283
850
425
1276
638
319
958
479
1438
719
2158
1079
3238
1619
4858
2429
7288
3644
1822
911
2734
1367
4102
2051
6154
3077
9232
4616
2308
1154
577
1732
866
433
1300
650
325
976
488
244
122
61
184
92
46
23
70
35
106
53
160
80
40
20
10
5
16
8
4
2
1
The hailstone sequence has length               112
77031 has the longest sequence of                351


## Plain TeX

The following code works with any TeX engine.

\newif\ifprint\newcount\itercount\newcount\currentnum\def\hailstone#1{\itercount=0 \currentnum=#1 \hailstoneaux}\def\hailstoneaux{%	\advance\itercount1	\ifprint\number\currentnum\space\space\fi	\ifnum\currentnum>1		\ifodd\currentnum			\multiply\currentnum3 \advance\currentnum1		\else			\divide\currentnum2		\fi		\expandafter\hailstoneaux	\fi} \parindent=0pt\printtrue\hailstone{27}Length = \number\itercount\bigbreak \newcount\ii \ii=1\printfalse\def\lenmax{0}\def\seed{0}\loop	\ifnum\ii<100000		\hailstone\ii		\ifnum\itercount>\lenmax\relax			\edef\lenmax{\number\itercount}%			\edef\seed{\number\ii}%		\fi		\advance\ii1\repeatSeed max = \seed, length = \lenmax\bye

pdf or dvi output:

27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206
103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167
502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619
4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732
866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16
8 4 2 1 Length = 112

Seed max = 77031, length = 351


## PowerShell

Works with: PowerShell version 3.0+
  function Get-HailStone {    param($n) switch($n) {        1              {$n;return} {$n % 2 -eq 0} {$n; return Get-Hailstone ($n = $n / 2)} {$n % 2 -ne 0} {$n; return Get-Hailstone ($n = ($n * 3) +1)} }} function Get-HailStoneBelowLimit { param($UpperLimit)     for ($i = 1;$i -lt $UpperLimit;$i++) {         [pscustomobject]@{            'Number' = $i 'Count' = (Get-HailStone$i).count        }     }}
Output:
PS C:\> Get-HailStone 27
27
82
41
...
8
4
2
1

PS C:\> (Get-HailStone 27).count
112

PS C:\> Get-HailStoneBelowLimit 100000 | Sort Count -Descending | Select -first 1
Number         Count
------         -----
77031           351

## Prolog

1. Create a routine to generate the hailstone sequence for a number.

hailstone(1,[1]) :- !.hailstone(N,[N|S]) :- 0 is N mod 2, N1 is N / 2, hailstone(N1,S).hailstone(N,[N|S]) :- 1 is N mod 2, N1 is (3 * N) + 1, hailstone(N1, S).

2. Use the routine to show that the hailstone sequence for the number 27 has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1.

The following query performs the test.

hailstone(27,X),length(X,112),append([27, 82, 41, 124], _, X),append(_, [8, 4, 2, 1], X).

3. Show the number less than 100,000 which has the longest hailstone sequence together with that sequences length.

longestHailstoneSequence(M, Seq, Len) :- longesthailstone(M, 1, 1, Seq, Len).longesthailstone(1, Cn, Cl, Mn, Ml):- Mn = Cn,	                               Ml = Cl.longesthailstone(N, _, Cl, Mn, Ml) :- hailstone(N, X),                                       length(X, L),                                       Cl < L,                                       N1 is N-1,                                       longesthailstone(N1, N, L, Mn, Ml).longesthailstone(N, Cn, Cl, Mn, Ml) :- N1 is N-1,                                       longesthailstone(N1, Cn, Cl, Mn, Ml).

run this query.

longestHailstoneSequence(100000, Seq, Len).

to get the following result

Seq = 77031,
Len = 351


### Constraint Handling Rules

CHR is a programming language created by Professor Thom Frühwirth.
Works with SWI-Prolog and module chr written by Tom Schrijvers and Jan Wielemaker

:- use_module(library(chr)).:- chr_option(debug, off).:- chr_option(optimize, full). :- chr_constraint collatz/2, hailstone/1, clean/0. % to remove all constraints hailstone/1 after computationclean @ clean \ hailstone(_) <=> true.clean @ clean <=> true. % compute Collatz numberinit @ collatz(1,X) <=>  X = 1 | true.collatz @ collatz(N, C) <=> (N mod 2 =:= 0 -> C is N / 2; C is 3 * N + 1). % Hailstone loophailstone(1) ==> true.hailstone(N) ==> N \= 1 | collatz(N, H), hailstone(H).

task1 :-	hailstone(27),	findall(X, find_chr_constraint(hailstone(X)), L),	clean,	% check the requirements	(   (length(L, 112), append([27, 82, 41, 124 | _], [8,4,2,1], L)) -> writeln(ok); writeln(ko)).
Output:
 ?- task1.
ok
true.

longest_sequence :-	seq(2, 100000, 1-[1], Len-V),	format('For ~w sequence has ~w len ! ~n', [V, Len]).  % walk through 2 to 100000 and compute the length of the sequences% memorize the longestseq(N, Max, Len-V, Len-V) :- N is Max + 1, !.seq(N, Max, CLen - CV, FLen - FV) :-	len_seq(N, Len - N),	(   Len > CLen -> Len1 = Len, V1 = [N]	;   Len = CLen -> Len1 = Len, V1 = [N | CV]	;   Len1 = CLen, V1 = CV),	N1 is N+1,	seq(N1, Max, Len1 - V1, FLen - FV). % compute the len of the Hailstone sequence for a numberlen_seq(N, Len - N) :-	hailstone(N),	findall(hailstone(X), find_chr_constraint(hailstone(X)), L),	length(L, Len),	clean.
Output:
 ?- longest_sequence.
For [77031] sequence has 351 len !
true.


## Pure

// 1. Create a routine to generate the hailstone sequence for a number. type odd x::int = x mod 2;type even x::int = ~odd x;odd x = typep odd x;even x = typep even x; hailstone 1       = [1];hailstone n::even = n:hailstone (n div 2);hailstone n::odd  = n:hailstone (3*n + 1); // 2. Use the routine to show that the hailstone sequence for the number 27 //    has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1n = 27;hs = hailstone n;l = # hs;using system; printf     ("the hailstone sequence for the number %d has %d elements " +      "starting with %s and ending with %s\n")     (n, l, __str__ (hs!!(0..3)), __str__ ( hs!!((l-4)..l))); // 3. Show the number less than 100,000 which has the longest hailstone //    sequence together with that sequences length.printf ("the number under 100,000 with the longest sequence is %d " +         "with a sequence length of %d\n")       (foldr (\ (a,b) (c,d) -> if (b > d) then (a,b) else (c,d))              (0,0)              (map (\ x -> (x, # hailstone x)) (1..100000)));
Output:
the hailstone sequence for the number 27 has 112 elements starting with [27,82,41,124] and ending with [8,4,2,1]
the number under 100,000 with the longest sequence is 77031 with a sequence length of 351


## Python

### Procedural

def hailstone(n):    seq = [n]    while n>1:        n = 3*n + 1 if n & 1 else n//2        seq.append(n)    return seq if __name__ == '__main__':    h = hailstone(27)    assert len(h)==112 and h[:4]==[27, 82, 41, 124] and h[-4:]==[8, 4, 2, 1]    print("Maximum length %i was found for hailstone(%i) for numbers <100,000" %          max((len(hailstone(i)), i) for i in range(1,100000)))
Output:
Maximum length 351 was found for hailstone(77031) for numbers <100,000

### Composition of pure functions

'''Hailstone sequences''' from itertools import (islice, takewhile)  # hailstone :: Int -> [Int]def hailstone(x):    '''Hailstone sequence starting with x.'''    def p(n):        return 1 != n    return list(takewhile(p, iterate(collatz)(x))) + [1]  # collatz :: Int -> Intdef collatz(n):    '''Next integer in the hailstone sequence.'''    return 3 * n + 1 if n & 1 else n // 2  # TEST ---------------------------------------------------- # main :: IO ()def main():    '''Tests.'''     n = 27    xs = hailstone(n)    print(unlines([        f'The hailstone sequence for {n} has {len(xs)} elements,',        f'starting with {take(4)(xs)},',        f'and ending with {drop(len(xs) - 4)(xs)}.\n'    ]))     (a, b) = (1, 99999)    (i, x) = max(        enumerate(            map(compose(len)(hailstone), enumFromTo(a)(b))        ),        key=snd    )    print(unlines([        f'The number in the range {a}..{b} '        f'which produces the longest sequence is {1 + i},',        f'generating a hailstone sequence of {x} integers.'    ]))  # GENERIC ------------------------------------------------  # compose (<<<) :: (b -> c) -> (a -> b) -> a -> cdef compose(g):    '''Function composition.'''    return lambda f: lambda x: g(f(x))  # drop :: Int -> [a] -> [a]# drop :: Int -> String -> Stringdef drop(n):    '''The sublist of xs beginning at (zero-based) index n.'''    def go(xs):        if isinstance(xs, list):            return xs[n:]        else:            take(n)(xs)            return xs    return lambda xs: go(xs)  # enumFromTo :: (Int, Int) -> [Int]def enumFromTo(m):    '''Integer enumeration from m to n.'''    return lambda n: list(range(m, 1 + n))  # iterate :: (a -> a) -> a -> Gen [a]def iterate(f):    '''An infinite list of repeated applications of f to x.'''    def go(x):        v = x        while True:            yield v            v = f(v)    return lambda x: go(x)  # snd :: (a, b) -> bdef snd(tpl):    '''Second component of a tuple.'''    return tpl[1]  # take :: Int -> [a] -> [a]# take :: Int -> String -> Stringdef take(n):    '''The prefix of xs of length n,       or xs itself if n > length xs.'''    return lambda xs: (        xs[0:n]        if isinstance(xs, list)        else list(islice(xs, n))    )  # unlines :: [String] -> Stringdef unlines(xs):    '''A single newline-delimited string derived       from a list of strings.'''    return '\n'.join(xs)  if __name__ == '__main__':    main()
Output:
The hailstone sequence for 27 has 112 elements,
starting with [27, 82, 41, 124],
and ending with [8, 4, 2, 1].

The number in the range 1..99999 which produces the longest sequence is 77031,
generating a hailstone sequence of 351 integers.

## R

### PART 1:makeHailstone <- function(n){  hseq <- n    while (hseq[length(hseq)] > 1){    current.value <- hseq[length(hseq)]    if (current.value %% 2 == 0){      next.value <- current.value / 2    } else {      next.value <- (3 * current.value) + 1    }    hseq <- append(hseq, next.value)  }  return(list(hseq=hseq, seq.length=length(hseq)))} ### PART 2:twenty.seven <- makeHailstone(27)twenty.seven$hseqtwenty.seven$seq.length ### PART 3:max.length <- 0;  lower.bound <- 1;  upper.bound <- 100000 for (index in lower.bound:upper.bound){  current.hseq <- makeHailstone(index)    if (current.hseq$seq.length > max.length){ max.length <- current.hseq$seq.length    max.index  <- index  }} cat("Between ", lower.bound, " and ", upper.bound, ", the input of ",     max.index, " gives the longest hailstone sequence, which has length ",     max.length, ". \n", sep="")
Output:
> twenty.seven$hseq [1] 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 [16] 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 [31] 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 [46] 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 [61] 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 [76] 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 [91] 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 [106] 10 5 16 8 4 2 1 > twenty.seven$seq.length
[1] 112

Between 1 and 1e+05, the input of 77031 gives the longest hailstone sequence,
which has length 351.

## Racket

 #lang racket (define hailstone  (let ([t (make-hasheq)])    (hash-set! t 1 '(1))    (λ(n) (hash-ref! t n            (λ() (cons n (hailstone (if (even? n) (/ n 2) (+ (* 3 n) 1))))))))) (define h27 (hailstone 27))(printf "h(27) = ~s, ~s items\n"        (,@(take h27 4) ... ,@(take-right h27 4))        (length h27)) (define N 100000)(define longest  (for/fold ([m #f]) ([i (in-range 1 (add1 N))])    (define h (hailstone i))    (if (and m (> (cdr m) (length h))) m (cons i (length h)))))(printf "for x<=~s, ~s has the longest sequence with ~s items\n"        N (car longest) (cdr longest)) 
Output:
h(27) = (27 82 41 124 ... 8 4 2 1), 112 items
for x<=100000, 77031 has the longest sequence with 351 items


## REBOL

 hail: func [	"Returns the hailstone sequence for n"	n [integer!]	/local seq] [	seq: copy reduce [n]	while [n <> 1] [		append seq n: either n % 2 == 0 [n / 2] [3 * n + 1]	]	seq] hs27: hail 27print [	"the hail sequence of 27 has length" length? hs27	"and has the form " copy/part hs27 3 "..."	back back back tail hs27] maxN: maxLen: 0repeat n 99999 [	if (len: length? hail n) > maxLen [		maxN: n		maxLen: len	]] print [	"the number less than 100000 with the longest hail sequence is"	maxN "with length" maxLen]
Output:
the hail sequence of 27 has length 112 and has the form  27 82 41 ... 4 2 1
the number less than 100000 with the longest hail sequence is 77031 with length 351

## REXX

/*REXX program tests a  number  and also a  range for  hailstone  (Collatz)  sequences. */numeric digits 20                                /*be able to handle gihugeic numbers.  */parse arg x y .                                  /*get optional arguments from the C.L. */if x=='' | x==","   then x=     27               /*No  1st  argument?  Then use default.*/if y=='' | y==","   then y= 100000 - 1           /* "  2nd      "        "   "     "    */$=hailstone(x) /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 1▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/say x ' has a hailstone sequence of ' words($)say      '    and starts with: '                 subword($, 1, 4) " ∙∙∙"say ' and ends with: ∙∙∙' subword($, max(5, words($)-3))if y==0 then exit /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 2▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/sayw=0; do j=1 for y /*traipse through the range of numbers.*/ call hailstone j /*compute the hailstone sequence for J.*/ if #hs<=w then iterate /*Not big 'nuff? Then keep traipsing.*/ bigJ=j; w=#hs /*remember what # has biggest hailstone*/ end /*j*/say '(between 1 ──►' y") " bigJ ' has the longest hailstone sequence: ' wexit /*stick a fork in it, we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/hailstone: procedure expose #hs; parse arg n 1 s /*N and S: are set to the 1st argument.*/ do #hs=1 while n\==1 /*keep loop while N isn't unity. */ if n//2 then n=n*3 + 1 /*N is odd ? Then calculate 3*n + 1 */ else n=n%2 /*" " even? Then calculate fast ÷ */ s=s n /* [↑] % is REXX integer division. */ end /*#hs*/ /* [↑] append N to the sequence list*/ return s /*return the S string to the invoker.*/ output when using the default inputs: 27 has a hailstone sequence of 112 and starts with: 27 82 41 124 ∙∙∙ and ends with: ∙∙∙ 8 4 2 1 (between 1 ──► 99999) 77031 has the longest hailstone sequence: 351  ### optimized This version is over fifteen times faster than the previous (unoptimized) version. It makes use of: • previously calculated Collatz sequences (memoization) • a faster method of determining if an integer is even /*REXX program tests a number and also a range for hailstone (Collatz) sequences. */!.=0; !.0=1; !.2=1; !.4=1; !.6=1; !.8=1 /*assign even numerals to be "true". */numeric digits 20; @.=0 /*handle big numbers; initialize array.*/parse arg x y z .; !.h=y /*get optional arguments from the C.L. */if x=='' | x=="," then x= 27 /*No 1st argument? Then use default.*/if y=='' | y=="," then y=100000 - 1 /* " 2nd " " " " */if z=='' | z=="," then z= 12 /*head/tail number? " " " */hm=max(y, 40000) /*use memoization (maximum num for @.)*/$=hailstone(x)      /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 1▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/say  x   ' has a hailstone sequence of '         words($)say ' and starts with: ' subword($, 1, z)    " ∙∙∙"say      '    and  ends  with:  ∙∙∙'             subword($, max(z+1, words($)-z+1))if y==0  then exit  /*▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒task 2▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒*/sayw=0;         do j=1  for y;  $=hailstone(j) /*traipse through the range of numbers.*/ #hs=words($)                        /*find the length of the hailstone seq.*/             if #hs<=w  then iterate             /*Not big enough?  Then keep traipsing.*/             bigJ=j;    w=#hs                    /*remember what # has biggest hailstone*/             end   /*j*/say '(between 1 ──►'   y") "        bigJ       ' has the longest hailstone sequence: '   wexit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/hailstone: procedure expose @. !. hm;  parse arg n 1 s 1 o,@.1  /*N,S,O: are the 1st arg*/                       do  while @.n==0          /*loop while the residual is unknown.  */                       parse var  n  ''  -1  L   /*extract the last decimal digit of  N.*/                       if !.L  then n=n%2        /*N is even?   Then calculate  fast ÷  */                               else n=n*3 + 1    /*"  " odd ?     "      "      3*n + 1 */                       s=s  n                    /* [↑]  %: is the REXX integer division*/                       end   /*while*/           /* [↑]  append  N  to the sequence list*/           s=s  @.n                              /*append the number to a sequence list.*/           @.o=subword(s, 2);    parse var s _ r /*use memoization for this hailstone #.*/              do  while r\=='';  parse var r _ r /*obtain the next  hailstone sequence. */              if @._\==0  then leave             /*Was number already found?  Return  S.*/              if _>hm     then iterate           /*Is  number  out of range?  Ignore it.*/              @._=r                              /*assign subsequence number to array.  */              end   /*while*/           return s
output   when using the default inputs:
27  has a hailstone sequence of  112
and starts with:  27 82 41 124 62 31 94 47 142 71 214 107  ∙∙∙
and  ends  with:  ∙∙∙ 53 160 80 40 20 10 5 16 8 4 2 1

(between 1─► 99999)  77031  has the longest hailstone sequence:  351


output   when using the inputs:   ,   1000000

27  has a hailstone sequence of  112
and starts with:  27 82 41 124 62 31 94 47 142 71 214 107  ∙∙∙
and  ends  with:  ∙∙∙ 53 160 80 40 20 10 5 16 8 4 2 1

(between 1 ──► 1000000)  837799  has the longest hailstone sequence:  525


## Ring

 size = 27aList = []hailstone(size) func hailstone n      add(aList,n)     while n != 1            if n % 2 = 0  n = n / 2           else n = 3 * n + 1 ok             add(aList, n)                   end        see "first 4 elements : "          for i = 1 to 4         see "" + aList[i]  + " "     next     see nl     see "last 4 elements : "     for i = len(aList) - 3 to len(aList)         see "" + aList[i] + " "     next 

## Ruby

This program uses new methods (Integer#even? and Enumerable#max_by) from Ruby 1.8.7.

Works with: Ruby version 1.8.7
def hailstone n  seq = [n]  until n == 1    n = (n.even?) ? (n / 2) : (3 * n + 1)    seq << n  end  seqend puts "for n = 27, show sequence length and first and last 4 elements"hs27 = hailstone 27p [hs27.length, hs27[0..3], hs27[-4..-1]] # find the longest sequence among n less than 100,000n = (1 ... 100_000).max_by{|n| hailstone(n).length}puts "#{n} has a hailstone sequence length of #{hailstone(n).length}"puts "the largest number in that sequence is #{hailstone(n).max}"
Output:
for n = 27, show sequence length and first and last 4 elements
[112, [27, 82, 41, 124], [8, 4, 2, 1]]
77031 has a hailstone sequence length of 351
the largest number in that sequence is 21933016


### With shared structure

This version builds some linked lists with shared structure. Hailstone::ListNode is an adaptation of ListNode from Singly-linked list/Element definition#Ruby. When two sequences contain the same value, those two lists share a tail. This avoids recomputing the end of the sequence.

Works with: Ruby version 1.8.7
module Hailstone  ListNode = Struct.new(:value, :size, :succ) do    def each      node = self      while node        yield node.value        node = node.succ      end    end  end   @@sequence = {1 => ListNode[1,1]}   module_function   def sequence(n)    unless @@sequence[n]      m, ary = n, []      until succ = @@sequence[m]        ary << m        m = m.even? ? (m / 2) : (3 * m + 1)      end      ary.reverse_each do |m|        @@sequence[m] = succ = ListNode[m, succ.size + 1, succ]      end    end    @@sequence[n]  endend puts "for n = 27, show sequence length and first and last 4 elements"hs27 = Hailstone.sequence(27).entriesp [hs27.size, hs27[0..3], hs27[-4..-1]] # find the longest sequence among n less than 100,000n = (1 ... 100_000).max_by{|n| Hailstone.sequence(n).size}puts "#{n} has a hailstone sequence length of #{Hailstone.sequence(n).size}"puts "the largest number in that sequence is #{Hailstone.sequence(n).max}"

output is the same as the above.

## Rust

fn hailstone(start : u32) -> Vec<u32> {    let mut res = Vec::new();    let mut next = start;     res.push(start);     while next != 1  {        next = if next % 2 == 0 { next/2 } else { 3*next+1 };        res.push(next);    }    res}  fn main() {    let test_num = 27;    let test_hailseq = hailstone(test_num);     println!("For {} number of elements is {} ", test_num, test_hailseq.len());     let fst_slice = test_hailseq[0..4].iter()                        .fold("".to_owned(), |acc, i| { acc + &*(i.to_string()).to_owned() + ", " });    let last_slice = test_hailseq[test_hailseq.len()-4..].iter()                        .fold("".to_owned(), |acc, i| { acc + &*(i.to_string()).to_owned() + ", " });     println!("  hailstone starting with {} ending with {} ", fst_slice, last_slice);     let max_range = 100000;    let mut max_len = 0;    let mut max_seed = 0;    for i_seed in 1..max_range {        let i_len = hailstone(i_seed).len();         if i_len > max_len {            max_len = i_len;            max_seed = i_seed;        }    }    println!("Longest sequence is {} element long for seed {}", max_len, max_seed);}
Output:
For 27 number of elements is 112
hailstone starting with 27, 82, 41, 124,  ending with 8, 4, 2, 1,
Longest sequence is 351 element long for seed 77031

## S-lang

% lst=1, return list of elements; lst=0 just return lengthdefine hailstone(n, lst){  variable l;  if (lst) l = {n};  else l = 1;   while (n > 1) {    if (n mod 2)      n = 3 * n + 1;    else      n /= 2;    if (lst)      list_append(l, n);    else      l++;    % if (prn) () = printf("%d, ", n);  }  % if (prn) () = printf("\n");  return l;} variable har = list_to_array(hailstone(27, 1)), more = 0;() = printf("Hailstone(27) has %d elements starting with:\n\t", length(har)); foreach $1 (har[[0:3]]) () = printf("%d, ",$1); () = printf("\nand ending with:\n\t");foreach $1 (har[[length(har)-4:]]) { if (more) () = printf(", "); more = printf("%d",$1);} () = printf("\ncalculating...\r");variable longest, longlen = 0, h;_for $1 (2, 99999, 1) {$2 = hailstone($1, 0); if ($2 > longlen) {    longest = $1; longlen =$2;    () = printf("longest sequence started w/%d and had %d elements  \r", longest, longlen);  }}() = printf("\n");
Output:
Hailstone(27) has 112 elements starting with:
27, 82, 41, 124,
and ending with:
8, 4, 2, 1
longest sequence started w/77031 and had 351 elements

## SAS

 * Create a routine to generate the hailstone sequence for one number;%macro gen_seq(n);   data hailstone;      array hs_seq(100000);      n=&n;      do until (n=1);         seq_size + 1;         hs_seq(seq_size) = n;         if mod(n,2)=0 then n=n/2;         else n=(3*n)+1;       end;	  seq_size + 1;      hs_seq(seq_size)=n;	  call symputx('seq_length',seq_size);   run;    proc sql;      title "First and last elements of Hailstone Sequence for number &n";	  select seq_size as sequence_length, hs_seq1, hs_seq2, hs_seq3, hs_seq4			%do i=&seq_length-3 %to &seq_length;				, hs_seq&i			%end; 		from hailstone;	quit;%mend; * Use the routine to output the first and last four numbers in the sequence for 27;%gen_seq(27); * Show the number less than 100,000 which has the longest hailstone sequence, and what that length is ;%macro longest_hailstone(start_num, end_num);	data hailstone_analysis;	  do start=&start_num to &end_num;	    n=start;		length_of_sequence=1;		do while (n>1);		  length_of_sequence+1;		  if mod(n,2)=0 then n=n/2;		  else n=(3*n) + 1;		end;		output;	  end;	run; 	proc sort data=hailstone_analysis;	  by descending length_of_sequence;	run; 	proc print data=hailstone_analysis (obs=1) noobs;	  title "Number from &start_num to &end_num with longest Hailstone sequence";	  var start length_of_sequence;	run;%mend;%longest_hailstone(1,99999); 
Output:
                   First and last elements of Hailstone Sequence for number 27
sequence_
length   hs_seq1   hs_seq2   hs_seq3   hs_seq4  hs_seq109  hs_seq110  hs_seq111  hs_seq112
-------------------------------------------------------------------------------------------------
112        27        82        41       124          8          4          2          1

Number from 1 to 99999 with longest Hailstone sequence
length_of_
start     sequence
77031        351


## Scala

Library: Scala
Works with: Scala version 2.10.2
object HailstoneSequence extends App {  def hailstone(n: Int): Stream[Int] =    n #:: (if (n == 1) Stream.empty else hailstone(if (n % 2 == 0) n / 2 else n * 3 + 1))   val nr = args.headOption.map(_.toInt).getOrElse(27)  val collatz = hailstone(nr)  println(s"Use the routine to show that the hailstone sequence for the number: $nr.") println(collatz.toList) println(s"It has${collatz.length} elements.")  println  println(    "Compute the number < 100,000, which has the longest hailstone sequence with that sequence's length.")  val (n, len) = (1 until 100000).map(n => (n, hailstone(n).length)).maxBy(_._2)  println(s"Longest hailstone sequence length= $len occurring with number$n.")}
Output:
Use the routine to show that the hailstone sequence for the number: 27.
List(27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1)
It has 112 elements.

Compute the number < 100,000, which has the longest hailstone sequence with that sequence's length.
Longest hailstone sequence length= 351 occurring with number 77031.

## Scheme

(define (collatz n)(if (= n 1) '(1)(cons n (collatz (if (even? n) (/ n 2) (+ 1 (* 3 n))))))) (define (collatz-length n)(let aux ((n n) (r 1)) (if (= n 1) r(aux (if (even? n) (/ n 2) (+ 1 (* 3 n))) (+ r 1))))) (define (collatz-max a b)(let aux ((i a) (j 0) (k 0))(if (> i b) (list j k)(let ((h (collatz-length i)))(if (> h k) (aux (+ i 1) i h) (aux (+ i 1) j k)))))) (collatz 27); (27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182; 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395; 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283; 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429; 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154; 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35; 106 53 160 80 40 20 10 5 16 8 4 2 1) (collatz-length 27); 112 (collatz-max 1 100000); (77031 351)

## Scilab

Translation of: MATLAB
function x=hailstone(n)    // iterative definition    // usage: global verbose; verbose=%T; hailstone(27)    global verbose    x=0; loop=%T    while(loop)         x=x+1        if verbose then            printf('%i ',n)        end        if n==1 then            loop=%F        elseif modulo(n,2)==1 then            n=3*n+1        else             n=n/2        end    endendfunction global verbose;verbose=1;N=hailstone(27);printf('\n\n%i\n',N); global verbose;verbose=0;N=100000;M=zeros(N,1);for k=1:N  M(k)=hailstone(k);end;[maxLength,n]=max(M)
Output:
27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
112
n  =      77031.
maxLength  =      351.  

$include "seed7_05.s7i"; const func array integer: hailstone (in var integer: n) is func result var array integer: hSequence is 0 times 0; begin while n <> 1 do hSequence &:= n; if odd(n) then n := 3 * n + 1; else n := n div 2; end if; end while; hSequence &:= n; end func; const func integer: hailstoneSequenceLength (in var integer: n) is func result var integer: sequenceLength is 1; begin while n <> 1 do incr(sequenceLength); if odd(n) then n := 3 * n + 1; else n := n div 2; end if; end while; end func; const proc: main is func local var integer: number is 0; var integer: length is 0; var integer: maxLength is 0; var integer: numberOfMaxLength is 0; var array integer: h27 is 0 times 0; begin for number range 1 to 99999 do length := hailstoneSequenceLength(number); if length > maxLength then maxLength := length; numberOfMaxLength := number; end if; end for; h27 := hailstone(27); writeln("hailstone(27):"); for number range 1 to 4 do write(h27[number] <& ", "); end for; write("...."); for number range length(h27) -3 to length(h27) do write(", " <& h27[number]); end for; writeln(" length=" <& length(h27)); writeln("Maximum length " <& maxLength <& " at number=" <& numberOfMaxLength); end func; Output: hailstone(27): 27, 82, 41, 124, ...., 8, 4, 2, 1 length=112 Maximum length 351 at number=77031  ## Sidef func hailstone (n) { var sequence = [n] while (n > 1) { sequence << ( n.is_even ? n.div!(2) : n.mul!(3).add!(1) ) } return(sequence)} # The hailstone sequence for the number 27var arr = hailstone(var nr = 27)say "#{nr}: #{arr.first(4)} ... #{arr.last(4)} (#{arr.len})" # The longest hailstone sequence for a number less than 100,000var h = [0, 0]for i (1 .. 99_999) { (var l = hailstone(i).len) > h[1] && ( h = [i, l] )} printf("%d: (%d)\n", h...) ## Smalltalk Works with: GNU Smalltalk Object subclass: Sequences [ Sequences class >> hailstone: n [ |seq| seq := OrderedCollection new. seq add: n. (n = 1) ifTrue: [ ^seq ]. (n even) ifTrue: [ seq addAll: (Sequences hailstone: (n / 2)) ] ifFalse: [ seq addAll: (Sequences hailstone: ( (3*n) + 1 ) ) ]. ^seq. ] Sequences class >> hailstoneCount: n [ ^ (Sequences hailstoneCount: n num: 1) ] "this 'version' avoids storing the sequence, it just counts its length - no memoization anyway" Sequences class >> hailstoneCount: n num: m [ (n = 1) ifTrue: [ ^m ]. (n even) ifTrue: [ ^ Sequences hailstoneCount: (n / 2) num: (m + 1) ] ifFalse: [ ^ Sequences hailstoneCount: ( (3*n) + 1) num: (m + 1) ]. ]]. |r|r := Sequences hailstone: 27. "hailstone 'from' 27"(r size) displayNl. "its length" "test 'head' ..."( (r first: 4) = #( 27 82 41 124 ) asOrderedCollection ) displayNl. "... and 'tail'"( ( (r last: 4 ) ) = #( 8 4 2 1 ) asOrderedCollection) displayNl. |longest|longest := OrderedCollection from: #( 1 1 ).2 to: 100000 do: [ :c | |l| l := Sequences hailstoneCount: c. (l > (longest at: 2) ) ifTrue: [ longest replaceFrom: 1 to: 2 with: { c . l } ].]. ('Sequence generator %1, sequence length %2' % { (longest at: 1) . (longest at: 2) }) displayNl. ## SNUSP  /@[email protected]@@+++# 27 | halve odd /===count<<\ /recurse\ #/?\ zero$>@/===!/===-?\==>?!/-<+++\    \!/=!\@\>?!\@/<@\.!\-/
/+<-\!>\?-<+>/++++<\?>+++/*6+4  |    |   \=/  \[email protected]@@[email protected]+++++#
\=>?/<=!=\   |                  |    !     /+ !/+ !/+ !/+   \    mod10
|//!==/========\         |    /<+> -\!?-\!?-\!?-\!?-\!
/=>?\<=/\<+>!\->+>+<<?/>>[email protected]/\ln \?!\-?!\-?!\-?!\-?!\-?/\    div10
\+<-/!<     ----------.++++++++++/      #  +/! +/! +/! +/! +/


## Swift

 func hailstone(var n:Int) -> [Int] {     var arr = [n]     while n != 1 {         if n % 2 == 0 {            n /= 2        } else {            n = (3 * n) + 1        }             arr.append(n)    }     return arr} let n = hailstone(27) println("hailstone(27): \(n[0...3]) ... \(n[n.count-4...n.count-1]) for a count of \(n.count).") var longest = (n: 1, len: 1) for i in 1...100_000 {     let new = hailstone(i)     if new.count > longest.len {        longest = (i, new.count)    }} println("Longest sequence for numbers under 100,000 is with \(longest.n). Which has \(longest.len) items.")
Output:
hailstone(27): [27, 82, 41, 124] ... [8, 4, 2, 1] for a count of 112
Longest sequence for numbers under 100,000 is with 77031. Which has 351 items.


## Tcl

The core looping structure is an example of an n-plus-one-half loop, except the loop is officially infinite here.

proc hailstone n {    while 1 {	lappend seq $n if {$n == 1} {return $seq} set n [expr {$n & 1 ? $n*3+1 :$n/2}]    }} set h27 [hailstone 27]puts "h27 len=[llength $h27]"puts "head4 = [lrange$h27 0 3]"puts "tail4 = [lrange $h27 end-3 end]" set maxlen [set max 0]for {set i 1} {$i<100000} {incr i} {    set l [llength [hailstone $i]] if {$l>$maxlen} {set maxlen$l;set max $i}}puts "max is$max, with length $maxlen" Output: h27 len=112 head4 = 27 82 41 124 tail4 = 8 4 2 1 max is 77031, with length 351  ## TI-83 BASIC ### Task 1 prompt NN→M: 0→X: 1→LWhile L=1X+1→XDisp MIf M=1 Then: 0→LElseIf remainder(M,2)=1Then: 3*M+1→MElse: M/2→MEndEndEnd{N,X} Output:  10 5 16 8 4 2 1 {27,112} ### Task 2 As the calculator is quite slow, so the output is for N=200 prompt N0→A:0→Bfor(I,1,N)I→M: 0→X: 1→LWhile L=1X+1→XIf M=1Then: 0→LElseIf remainder(M,2)=1Then: 3*M+1→MElse: M/2→MEndEndEndIf X>B: ThenI→A:X→BEndDisp {I,X}End{A,B} Output: {171,125} ## TXR @(do (defun hailstone (n) (cons n (gen (not (eq n 1)) (set n (if (evenp n) (trunc n 2) (+ (* 3 n) 1)))))))@(next :list @(mapcar* (fun tostring) (hailstone 27)))278241124@(skip)8421@(eof)@(do (let ((max 0) maxi) (each* ((i (range 1 99999)) (h (mapcar* (fun hailstone) i)) (len (mapcar* (fun length) h))) (if (> len max) (progn (set max len) (set maxi i)))) (format t "longest sequence is ~a for n = ~a\n" max maxi))) $ txr -l hailstone.txr
longest sequence is 351 for n = 77031

## uBasic/4tH

Translation of: FreeBASIC
' ------=< MAIN >=------ m = 0Proc _hailstone_print(27)Print For x = 1 To 10000    n = Func(_hailstone(x))    If n > m Then        t = x        m = n    EndIfNext Print  "The longest sequence is for "; t; ", it has a sequence length of "; m End _hailstone_print Param (1)    ' print the number and sequence     Local (1)    [email protected] = 1     Print "sequence for number "; [email protected]    Print Using "________"; [email protected];   'starting number     Do While [email protected] # 1        If ([email protected] % 2 ) = 1 Then            [email protected] = [email protected] * 3 + 1   ' n * 3 + 1        Else            [email protected] = [email protected] / 2       ' n / 2        EndIf         [email protected] = [email protected] + 1        Print Using "________"; [email protected];         If ([email protected] % 10) = 0 Then Print    Loop     Print : Print    Print "sequence length = "; [email protected]    Print     For [email protected] = 0 To 79      Print "-";    Next     PrintReturn _hailstone Param (1)    ' normal version    ' only counts the sequence     Local (1)    [email protected] = 1     Do While [email protected] # 1        If ([email protected] % 2) = 1 Then            [email protected] = [email protected] * 3 + 1  ' n * 3 + 1        Else            [email protected] = [email protected] / 2      ' divide number by 2        EndIf         [email protected] = [email protected] + 1    Loop Return ([email protected])

uBasic is an interpreted language. Doing a sequence up to 100,000 would take over an hour, so we did up to 10,000 here.

Output:
sequence for number 27
27      82      41     124      62      31      94      47     142      71
214     107     322     161     484     242     121     364     182      91
274     137     412     206     103     310     155     466     233     700
350     175     526     263     790     395    1186     593    1780     890
445    1336     668     334     167     502     251     754     377    1132
566     283     850     425    1276     638     319     958     479    1438
719    2158    1079    3238    1619    4858    2429    7288    3644    1822
911    2734    1367    4102    2051    6154    3077    9232    4616    2308
1154     577    1732     866     433    1300     650     325     976     488
244     122      61     184      92      46      23      70      35     106
53     160      80      40      20      10       5      16       8       4
2       1

sequence length = 112
--------------------------------------------------------------------------------
The longest sequence is for 6171, it has a sequence length of 262



## UNIX Shell

The best way is to use a shell with built-in arrays and arithmetic, such as Bash.

Works with: Bash
#!/bin/bash# seq is the array genereated by hailstone# index is used for seqdeclare -a seqdeclare -i index # Create a routine to generate the hailstone sequence for a numberhailstone () {  unset seq index  seq[$((index++))]=$((n=$1)) while [$n -ne 1 ]; do    [ $((n % 2)) -eq 1 ] && ((n=n*3+1)) || ((n=n/2)) seq[$((index++))]=$n done} # Use the routine to show that the hailstone sequence for the number 27# has 112 elements starting with 27, 82, 41, 124 and ending with 8, 4, 2, 1i=27hailstone$iecho "$i:${#seq[@]}"echo "${seq[@]:0:4} ...${seq[@]:(-4):4}" # Show the number less than 100,000 which has the longest hailstone# sequence together with that sequences length.# (But don't show the actual sequence)!max=0maxlen=0for ((i=1;i<100000;i++)); do  hailstone $i if [$((len=${#seq[@]})) -gt$maxlen ]; then    max=$i maxlen=$len  fidone echo "${max} has a hailstone sequence length of${maxlen}"
Output:
27: 112
27 82 41 124 ... 8 4 2 1
77031 has a hailstone sequence of 351

### Bourne Shell

This script follows tradition for the Bourne Shell; its hailstone() function writes the sequence to standard output, so the shell can capture or pipe this output. This script is very slow because it forks many processes. Each command substitution forks a subshell, and each expr(1) command forks a process.

• Therefore, this script only examines sequences from 1 to 1000, not 100000. A fast computer might run this script in 45 to 120 seconds, using most time to run system calls in kernel mode. If the script went to 100000, it would need several hours.
Works with: Bourne Shell
# Outputs a hailstone sequence from $1, with one element per line.# Clobbers$n.hailstone() {	n=expr "$1" + 0 eval "test$? -lt 2 || return $?" #$n must be integer. 	echo $n while test$n -ne 1; do		if expr $n % 2 >/dev/null; then n=expr 3 \*$n + 1		else			n=expr $n / 2 fi echo$n	done} set -- hailstone 27echo "Hailstone sequence from 27 has $# elements:"first="$1, $2,$3, $4"shift expr$# - 4echo "  $first, ...,$1, $2,$3, $4" i=1 max=0 maxlen=0while test$i -lt 1000; do	len=hailstone $i | wc -l | tr -d ' ' test$len -gt $maxlen && max=$i maxlen=$len i=expr$i + 1doneecho "Hailstone sequence from $max has$maxlen elements."

### C Shell

This script is several times faster than the previous Bourne Shell script, because it uses C Shell expressions, not the expr(1) command. This script is slow, but it can reach 100000, and a fast computer might run it in less than 15 minutes.

# Outputs a hailstone sequence from !:1, with one element per line.# Clobbers $n.alias hailstone eval \''@ n = \!:1:q \\ echo$n					\\	while ( $n != 1 ) \\ if ($n % 2 ) then		\\			@ n = 3 * $n + 1 \\ else \\ @ n /= 2 \\ endif \\ echo$n				\\	end					\\'\' set sequence=(hailstone 27)echo "Hailstone sequence from 27 has $#sequence elements:"@ i =$#sequence - 3echo "  $sequence[1-4] ...$sequence[$i-]" # hailstone-length$i#   acts like# @ len = hailstone $i | wc -l | tr -d ' '# but without forking any subshells.alias hailstone-length eval \''@ n = \!:1:q \\ @ len = 1 \\ while ($n != 1 )			\\		if ( $n % 2 ) then \\ @ n = 3 *$n + 1	\\		else				\\			@ n /= 2		\\		endif				\\		@ len += 1			\\	end					\\'\' @ i = 1@ max = 0@ maxlen = 0while ($i < 100000) # XXX - I must run hailstone-length in a subshell, because my # C Shell has a bug when it runs hailstone-length inside this # while ($i < 1000) loop: it forgets about this loop, and	# reports an error <<end: Not in while/foreach.>>	@ len = hailstone-length $i; echo$len	if ($len >$maxlen) then		@ max = $i @ maxlen =$len	endif	@ i += 1endecho "Hailstone sequence from $max has$maxlen elements."
Output:
$csh -f hailstone.csh Hailstone sequence from 27 has 112 elements: 27 82 41 124 ... 8 4 2 1 Hailstone sequence from 77031 has 351 elements. ## Ursa ### Implementation hailstone.u import "math" def hailstone (int n) decl int<> seq while (> n 1) append n seq if (= (mod n 2) 0) set n (floor (/ n 2)) else set n (int (+ (* 3 n) 1)) end if end while append n seq return seqend hailstone ### Usage Output: > import "hailstone.u" > out (hailstone 27) endl console class java.lang.Integer<27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182, 91, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638, 319, 958, 479, 1438, 719, 2158, 1079, 3238, 1619, 4858, 2429, 7288, 3644, 1822, 911, 2734, 1367, 4102, 2051, 6154, 3077, 9232, 4616, 2308, 1154, 577, 1732, 866, 433, 1300, 650, 325, 976, 488, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1> > out (size (hailstone 27)) endl console 112 > decl int i max maxLoc > for (set i 1) (< i 100000) (inc i) .. decl int result .. set result (size (hailstone i)) .. .. if (> result max) .. set max result .. set maxLoc i .. end if ..end for > out "hailstone(" maxLoc ")= " max endl console hailstone(77031)= 351 > _ ## Ursala #import std#import nat hail = @iNC ~&h~=1->x ^C\~& @h ~&h?\~&t successor+ [email protected] #show+ main = < ^T(@ixX take/$4; %nLP~~lrxPX; ^|TL/~& :/'...',' has length '[email protected]+ %nP+ length) hail 27,   ^|TL(~&,:/' has sequence length ') %nP~~ nleq$^&r ^(~&,length+ hail)* nrange/1 100000> The hail function computes the sequence as follows. • Given a number as an argument, @iNC makes a list containing only that number before passing it to the rest of the function. The i in the expression stands for the identity function, N for the constant null function, and C for the cons operator. • The iteration combinator (->) is used with a predicate of ~&h~=l which tests the condition that the head (~&h) of its argument is not equal (~=) to 1. Iteration of the rest of the function continues while this predicate holds. • The x suffix says to return the reversal of the list after the iteration finishes. • The function being iterated builds a list using the cons operator (^C) with the identity function (~&) of the argument for the tail, and the result of the rest of the line for the head. • The @h operator says that the function following will be applied to the head of the list. • The conditional operator (?) has the head function (~&h) as its predicate, which tests whether the head of its argument is non-null. • In this case, the argument is a natural number, but naturals are represented as lists of booleans, so taking the head of a number is the same as testing the least significant bit. • If the condition is not met, the number has a 0 least significant bit, and therefore is even. In this case, the conditional predicate calls for taking its tail (~&t), effectively dividing it by 2 using a bit shift. • If the condition is met, the number is odd, so the rest of the function computes the successor of the number multiplied by three. • Rather than multiplying the hard way, the function [email protected] computes the sum of the pair (X) of numbers given by the identity function (i) of the argument, and the doubling of the argument (NiC), also obtained by a bit shift, with a zero bit (N) consed (C) with the identity (i). Most of the main expression pertains to less interesting printing and formatting, but the part that searches for the longest sequence in the range is nleq$^&r ^(~&,length+ hail)* nrange/1 100000.

• The expression nrange/1 100000 evaluates to the list of the first 100000 positive integers.
• The map operator (*) causes a list to be made of the results of its operand applied to each number.
• The operand to the map operator, applied to an individual number in the list, constructs a pair (^) with the identity function (~&) of the number on the left, and the length of the hail sequence on the right.
• The maximizing operator (\$^) with respect to the natural less or equal relation (nleq) applied to the right sides (&r) of its pair of arguments extracts the number with the maximum length sequence.
Output:
<27,82,41,124>...<8,4,2,1> has length 112
77031 has sequence length 351

## VBA

Translation of: Phix
Private Function hailstone(ByVal n As Long) As Collection    Dim s As New Collection    s.Add CStr(n), CStr(n)    i = 0    Do While n <> 1        If n Mod 2 = 0 Then            n = n / 2        Else            n = 3 * n + 1        End If        s.Add CStr(n), CStr(n)    Loop    Set hailstone = sEnd Function Private Function hailstone_count(ByVal n As Long)    Dim count As Long: count = 1    Do While n <> 1        If n Mod 2 = 0 Then            n = n / 2        Else            n = 3 * n + 1        End If        count = count + 1    Loop    hailstone_count = countEnd Function Public Sub rosetta()    Dim s As Collection, i As Long    Set s = hailstone(27)    Dim ls As Integer: ls = s.count    Debug.Print "hailstone(27) = ";    For i = 1 To 4        Debug.Print s(i); ", ";    Next i    Debug.Print "... ";    For i = s.count - 4 To s.count - 1        Debug.Print s(i); ", ";    Next i    Debug.Print s(s.count)    Debug.Print "length ="; ls    Dim hmax As Long: hmax = 1    Dim imax As Long: imax = 1    Dim count As Integer    For i = 2 To 100000# - 1        count = hailstone_count(i)        If count > hmax Then            hmax = count            imax = i        End If    Next i    Debug.Print "The longest hailstone sequence under 100,000 is"; imax; "with"; hmax; "elements."End Sub
Output:
hailstone(27) = 27, 82, 41, 124, ... 16, 8, 4, 2, 1
length = 112

The longest hailstone sequence under 100,000 is 77031 with 351 elements.

## VBScript

 'function arguments: "num" is the number to sequence and "return" is the value to return - "s" for the sequence or '"e" for the number elements.Function hailstone_sequence(num,return)    n = num	sequence = num	elements = 1	Do Until n = 1		If n Mod 2 = 0 Then			n = n / 2		Else			n = (3 * n) + 1		End If		sequence = sequence & " " & n		elements = elements + 1		Loop	Select Case return		Case "s"			hailstone_sequence = sequence		Case "e"			hailstone_sequence = elements	End SelectEnd Function 'test driving.'show sequence for 27WScript.StdOut.WriteLine "Sequence for 27: " & hailstone_sequence(27,"s")WScript.StdOut.WriteLine "Number of Elements: " & hailstone_sequence(27,"e")WScript.StdOut.WriteBlankLines(1)'show the number less than 100k with the longest sequencecount = 1n_elements = 0n_longest = ""Do While count < 100000	current_n_elements = hailstone_sequence(count,"e")	If current_n_elements > n_elements Then		n_elements = current_n_elements		n_longest = "Number: " & count & " Length: " & n_elements	End If	count = count + 1LoopWScript.StdOut.WriteLine "Number less than 100k with the longest sequence: "WScript.StdOut.WriteLine n_longest 
Output:
Sequence for 27: 27 82 41 124 62 31 94 47 142 71 214 107 322 161 484 242 121 364 182 91 274 137 412 206 103 310 155 466 233 700 350 175 526 263 790 395 1186 593 1780 890 445 1336 668 334 167 502 251 754 377 1132 566 283 850 425 1276 638 319 958 479 1438 719 2158 1079 3238 1619 4858 2429 7288 3644 1822 911 2734 1367 4102 2051 6154 3077 9232 4616 2308 1154 577 1732 866 433 1300 650 325 976 488 244 122 61 184 92 46 23 70 35 106 53 160 80 40 20 10 5 16 8 4 2 1
Number of Elements: 112

Number less than 100k with the longest sequence:
Number: 77031 Length: 351


## Visual Basic

Translation of: PL/I
Works with: Visual Basic version VB6 Standard
Option ExplicitDim flag As Boolean ' true to print valuesSub main()    Dim longest As Long, n As Long    Dim i As Long, value As Long    ' Task 1:    flag = True    i = 27    Debug.Print "The hailstone sequence has length of "; i; " is "; hailstones(i)    ' Task 2:    flag = False    longest = 0    For i = 1 To 99999        If longest < hailstones(i) Then            longest = hailstones(i)            value = i        End If    Next i    Debug.Print value; " has the longest sequence of "; longestEnd Sub 'mainFunction hailstones(n As Long) As Long    Dim m As Long, p As Long    Dim m1 As Long, m2 As Long, m3 As Long, m4 As Long    If flag Then Debug.Print "The sequence for"; n; "is: ";    p = 1    m = n    If flag Then Debug.Print m;    While m > 1        p = p + 1        If (m Mod 2) = 0 Then            m = m / 2        Else            m = 3 * m + 1        End If        If p <= 4 Then If flag Then Debug.Print m;        m4 = m3        m3 = m2        m2 = m1        m1 = m    Wend    If flag Then        If p <= 4 Then            Debug.Print        ElseIf p = 5 Then            Debug.Print m1        ElseIf p = 6 Then            Debug.Print m2; m1        ElseIf p = 7 Then            Debug.Print m3; m2; m1        ElseIf p = 8 Then            Debug.Print m4; m3; m2; m1        Else            Debug.Print "..."; m4; m3; m2; m1        End If    End If    hailstones = pEnd Function 'hailstones
Output:
The sequence for 27 is:  27  82  41  124 ... 8  4  2  1
The hailstone sequence has length of  27  is  112
77031  has the longest sequence of  351 

## Visual Basic .NET

Works with: Visual Basic .NET version 2005+
Module HailstoneSequence    Sub Main()        ' Checking sequence of 27.         Dim l As List(Of Long) = HailstoneSequence(27)        Console.WriteLine("27 has {0} elements in sequence:", l.Count())         For i As Integer = 0 To 3 : Console.Write("{0}, ", l(i)) : Next        Console.Write("... ")        For i As Integer = l.Count - 4 To l.Count - 1 : Console.Write(", {0}", l(i)) : Next         Console.WriteLine()         ' Finding longest sequence for numbers below 100000.         Dim max As Integer = 0        Dim maxCount As Integer = 0         For i = 1 To 99999            l = HailstoneSequence(i)            If l.Count > maxCount Then                max = i                maxCount = l.Count            End If        Next        Console.WriteLine("Max elements in sequence for number below 100k: {0} with {1} elements.", max, maxCount)        Console.ReadLine()    End Sub     Private Function HailstoneSequence(ByVal n As Long) As List(Of Long)        Dim valList As New List(Of Long)()        valList.Add(n)         Do Until n = 1            n = IIf(n Mod 2 = 0, n / 2, (3 * n) + 1)            valList.Add(n)        Loop         Return valList    End Function End Module
Output:
27 has 112 elements in sequence:
27, 82, 41, 124, ... , 8, 4, 2, 1
Max elements in sequence for number below 100k: 77031 with 351 elements.


## XPL0

include c:\cxpl\codes;  \intrinsic 'code' declarationsint Seq(1000);          \more than enough for longest sequence func Hailstone(N);      \Return length of Hailstone sequence starting at Nint  N;                 \ also fills Seq array with sequenceint  I;[I:= 0;loop [Seq(I):= N;  I:= I+1;     if N=1 then return I;     N:= if N&1 then N*3+1 else N/2;     ];]; int N, SN, Len, MaxLen;[Len:= Hailstone(27);Text(0, "27's Hailstone length = ");  IntOut(0, Len);  CrLf(0); Text(0, "Sequence = ");for N:= 0 to 3 do [IntOut(0, Seq(N));  ChOut(0, ^ )];Text(0, "... ");for N:= Len-4 to Len-1 do [IntOut(0, Seq(N));  ChOut(0, ^ )];CrLf(0); MaxLen:= 0;for N:= 1 to 100_000-1 do    [Len:= Hailstone(N);    if Len > MaxLen then [MaxLen:= Len;  SN:= N];       \save N with max length    ];IntOut(0, SN);  Text(0, "'s Hailstone length = ");  IntOut(0, MaxLen);]
Output:
27's Hailstone length = 112
Sequence = 27 82 41 124 ... 8 4 2 1
77031's Hailstone length = 351


## zkl

fcn collatz(n,z=L()){ z.append(n); if(n==1) return(z);   if(n.isEven) return(self.fcn(n/2,z)); return(self.fcn(n*3+1,z)) }

This uses tail recursion and thus is stack efficient.

Output:
var n=collatz(27)
n.len()
112
n[0,4]
L(27,82,41,124)
n[-4,*]
L(8,4,2,1)


Rather than write a function that calculates the length, just roll through all 100,000 sequences and save the largest (length,sequence start) pair. Creating all those Collatz lists isn't quick. This works by using a [mutable] list to hold state as the pump does the basic looping.

[2..0d100_000].pump(Void,  // loop n from 2 to 100,000   collatz,              // generate Collatz sequence(n)   fcn(c,n){           // if new longest sequence, save length/C, return longest      if(c.len()>n[0]) n.clear(c.len(),c[0]); n}.fp1(L(0,0)))
Output:
L(351,77031)  // length, hailstone


## ZX Spectrum Basic

Translation of: BBC_BASIC
10 LET n=27: LET s=120 GO SUB 100030 PRINT '"Sequence length = ";seqlen40 LET maxlen=0: LET s=050 FOR m=2 TO 10000060 LET n=m70 GO SUB 100080 IF seqlen>maxlen THEN LET maxlen=seqlen: LET maxnum=m90 NEXT m100 PRINT "The number with the longest hailstone sequence is ";maxnum110 PRINT "Its sequence length is ";maxlen120 STOP 1000 REM Hailstone1010 LET l=01020 IF s THEN PRINT n;"  ";1030 IF n=1 THEN LET seqlen=l+1: RETURN 1040 IF FN m(n,2)=0 THEN LET n=INT (n/2): GO TO 10601050 LET n=3*n+11060 LET l=l+11070 GO TO 10202000 DEF FN m(a,b)=a-INT (a/b)*b`