Factorions
You are encouraged to solve this task according to the task description, using any language you may know.
- Definition
A factorion is a natural number that equals the sum of the factorials of its digits.
- Example
145 is a factorion in base 10 because:
1! + 4! + 5! = 1 + 24 + 120 = 145
It can be shown (see talk page) that no factorion in base 10 can exceed 1,499,999.
- Task
Write a program in your language to demonstrate, by calculating and printing out the factorions, that:
- There are 3 factorions in base 9
- There are 4 factorions in base 10
- There are 5 factorions in base 11
- There are 2 factorions in base 12 (up to the same upper bound as for base 10)
11l
<lang 11l>V fact = [1] L(n) 1..11
fact.append(fact[n-1] * n)
L(b) 9..12
print(‘The factorions for base ’b‘ are:’) L(i) 1..1'499'999 V fact_sum = 0 V j = i L j > 0 V d = j % b fact_sum += fact[d] j I/= b I fact_sum == i print(i, end' ‘ ’) print("\n")</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
360 Assembly
<lang 360asm>* Factorions 26/04/2020 FACTORIO CSECT
USING FACTORIO,R13 base register B 72(R15) skip savearea DC 17F'0' savearea SAVE (14,12) save previous context ST R13,4(R15) link backward ST R15,8(R13) link forward LR R13,R15 set addressability XR R4,R4 ~ LA R5,1 f=1 LA R3,FACT+4 @fact(1) LA R6,1 i=1 DO WHILE=(C,R6,LE,=A(NN2)) do i=1 to nn2 MR R4,R6 fact(i-1)*i ST R5,0(R3) fact(i)=fact(i-1)*i LA R3,4(R3) @fact(i+1) LA R6,1(R6) i++ ENDDO , enddo i LA R7,NN1 base=nn1 DO WHILE=(C,R7,LE,=A(NN2)) do base=nn1 to nn2
MVC PG,PGX init buffer
LA R3,PG+6 @buffer XDECO R7,XDEC edit base MVC PG+5(2),XDEC+10 output base LA R3,PG+10 @buffer LA R6,1 i=1 DO WHILE=(C,R6,LE,LIM) do i=1 to lim LA R9,0 s=0 LR R8,R6 t=i DO WHILE=(C,R8,NE,=F'0') while t<>0 XR R4,R4 ~ LR R5,R8 t DR R4,R7 r5=t/base; r4=d=(t mod base) LR R1,R4 d SLA R1,2 ~ L R2,FACT(R1) fact(d) AR R9,R2 s=s+fact(d) LR R8,R5 t=t/base ENDDO , endwhile IF CR,R9,EQ,R6 THEN if s=i then XDECO R6,XDEC edit i MVC 0(6,R3),XDEC+6 output i LA R3,7(R3) @buffer ENDIF , endif LA R6,1(R6) i++ ENDDO , enddo i XPRNT PG,L'PG print buffer LA R7,1(R7) base++ ENDDO , enddo base L R13,4(0,R13) restore previous savearea pointer RETURN (14,12),RC=0 restore registers from calling save
NN1 EQU 9 nn1=9 NN2 EQU 12 nn2=12 LIM DC f'1499999' lim=1499999 FACT DC (NN2+1)F'1' fact(0:12) PG DS CL80 buffer PGX DC CL80'Base .. : ' buffer init XDEC DS CL12 temp fo xdeco
REGEQU END FACTORIO </lang>
- Output:
Base 9 : 1 2 41282 Base 10 : 1 2 145 40585 Base 11 : 1 2 26 48 40472 Base 12 : 1 2
ALGOL 68
<lang algol68>BEGIN
# cache factorials from 0 to 11 # [ 0 : 11 ]INT fact; fact[0] := 1; FOR n TO 11 DO fact[n] := fact[n-1] * n OD; FOR b FROM 9 TO 12 DO print( ( "The factorions for base ", whole( b, 0 ), " are:", newline ) ); FOR i TO 1500000 - 1 DO INT sum := 0; INT j := i; WHILE j > 0 DO sum +:= fact[ j MOD b ]; j OVERAB b OD; IF sum = i THEN print( ( whole( i, 0 ), " " ) ) FI OD; print( ( newline ) ) OD
END</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Applesoft BASIC
<lang basic>100 DIM FACT(12) 110 FACT(0) = 1 120 FOR N = 1 TO 11 130 FACT(N) = FACT(N - 1) * N 140 NEXT 200 FOR B = 9 TO 12 210 PRINT "THE FACTORIONS "; 215 PRINT "FOR BASE "B" ARE:" 220 FOR I = 1 TO 1499999 230 SUM = 0 240 FOR J = I TO 0 STEP 0 245 M = INT (J / B) 250 D = J - M * B 260 SUM = SUM + FACT(D) 270 J = M 280 NEXT J 290 IF SU = I THEN PRINT I" "; 300 NEXT I 310 PRINT : PRINT 320 NEXT B</lang>
AutoHotkey
<lang AutoHotkey>fact:=[] fact[0] := 1 while (A_Index < 12) fact[A_Index] := fact[A_Index-1] * A_Index b := 9 while (b <= 12) { res .= "base " b " factorions: `t" while (A_Index < 1500000){ sum := 0 j := A_Index while (j > 0){ d := Mod(j, b) sum += fact[d] j /= b } if (sum = A_Index) res .= A_Index " " } b++ res .= "`n" } MsgBox % res return</lang>
- Output:
base 9 factorions: 1 2 41282 base 10 factorions: 1 2 145 40585 base 11 factorions: 1 2 26 48 40472 base 12 factorions: 1 2
AWK
<lang AWK>
- syntax: GAWK -f FACTORIONS.AWK
- converted from C
BEGIN {
fact[0] = 1 # cache factorials from 0 to 11 for (n=1; n<12; ++n) { fact[n] = fact[n-1] * n } for (b=9; b<=12; ++b) { printf("base %d factorions:",b) for (i=1; i<1500000; ++i) { sum = 0 j = i while (j > 0) { d = j % b sum += fact[d] j = int(j/b) } if (sum == i) { printf(" %d",i) } } printf("\n") } exit(0)
} </lang>
- Output:
base 9 factorions: 1 2 41282 base 10 factorions: 1 2 145 40585 base 11 factorions: 1 2 26 48 40472 base 12 factorions: 1 2
C
<lang c>#include <stdio.h>
int main() {
int n, b, d; unsigned long long i, j, sum, fact[12]; // cache factorials from 0 to 11 fact[0] = 1; for (n = 1; n < 12; ++n) { fact[n] = fact[n-1] * n; }
for (b = 9; b <= 12; ++b) { printf("The factorions for base %d are:\n", b); for (i = 1; i < 1500000; ++i) { sum = 0; j = i; while (j > 0) { d = j % b; sum += fact[d]; j /= b; } if (sum == i) printf("%llu ", i); } printf("\n\n"); } return 0;
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
C++
<lang cpp>#include <iostream>
class factorion_t { public:
factorion_t() { f[0] = 1u; for (uint n = 1u; n < 12u; n++) f[n] = f[n - 1] * n; }
bool operator()(uint i, uint b) const { uint sum = 0; for (uint j = i; j > 0u; j /= b) sum += f[j % b]; return sum == i; }
private:
ulong f[12]; //< cache factorials from 0 to 11
};
int main() {
factorion_t factorion; for (uint b = 9u; b <= 12u; ++b) { std::cout << "factorions for base " << b << ':'; for (uint i = 1u; i < 1500000u; ++i) if (factorion(i, b)) std::cout << ' ' << i; std::cout << std::endl; } return 0;
}</lang>
- Output:
factorions for base 9: 1 2 41282 factorions for base 10: 1 2 145 40585 factorions for base 11: 1 2 26 48 40472 factorions for base 12: 1 2
Common Lisp
<lang lisp>(defparameter *bases* '(9 10 11 12)) (defparameter *limit* 1500000)
(defun ! (n) (apply #'* (loop for i from 2 to n collect i)))
(defparameter *digit-factorials* (mapcar #'! (loop for i from 0 to (1- (apply #'max *bases*)) collect i)))
(defun fact (n) (nth n *digit-factorials*))
(defun digit-value (digit)
(let ((decimal (digit-char-p digit))) (cond ((not (null decimal)) decimal) ((char>= #\Z digit #\A) (+ (char-code digit) (- (char-code #\A)) 10)) ((char>= #\z digit #\a) (+ (char-code digit) (- (char-code #\a)) 10)) (t nil))))
(defun factorionp (n &optional (base 10))
(= n (apply #'+ (mapcar #'fact (map 'list #'digit-value (write-to-string n :base base))))))
(loop for base in *bases* do
(let ((factorions (loop for i from 1 while (< i *limit*) if (factorionp i base) collect i))) (format t "In base ~a there are ~a factorions:~%" base (list-length factorions)) (loop for n in factorions do (format t "~c~a" #\Tab (write-to-string n :base base)) (if (/= base 10) (format t " (decimal ~a)" n)) (format t "~%")) (format t "~%")))</lang>
- Output:
In base 9 there are 3 factorions: 1 (decimal 1) 2 (decimal 2) 62558 (decimal 41282) In base 10 there are 4 factorions: 1 2 145 40585 In base 11 there are 5 factorions: 1 (decimal 1) 2 (decimal 2) 24 (decimal 26) 44 (decimal 48) 28453 (decimal 40472) In base 12 there are 2 factorions: 1 (decimal 1) 2 (decimal 2)
Delphi
<lang Delphi> program Factorions;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
begin
var fact: TArray<UInt64>; SetLength(fact, 12);
fact[0] := 0; for var n := 1 to 11 do fact[n] := fact[n - 1] * n;
for var b := 9 to 12 do begin writeln('The factorions for base ', b, ' are:'); for var i := 1 to 1499999 do begin var sum := 0; var j := i; while j > 0 do begin var d := j mod b; sum := sum + fact[d]; j := j div b; end; if sum = i then writeln(i, ' '); end; writeln(#10); end; readln;
end.</lang>
F#
<lang fsharp> // Factorians. Nigel Galloway: October 22nd., 2021 let N=[|let mutable n=1 in yield n; for g in 1..11 do n<-n*g; yield n|] let fG n g=let rec fN g=function i when i<n->g+N.[i] |i->fN(g+N.[i%n])(i/n) in fN 0 g {9..12}|>Seq.iter(fun n->printf $"In base %d{n} Factorians are:"; {1..1500000}|>Seq.iter(fun g->if g=fG n g then printf $" %d{g}"); printfn "") </lang>
- Output:
In base 9 Factorians are: 1 2 41282 In base 10 Factorians are: 1 2 145 40585 In base 11 Factorians are: 1 2 26 48 40472 In base 12 Factorians are: 1 2
Factor
<lang factor>USING: formatting io kernel math math.parser math.ranges memoize prettyprint sequences ; IN: rosetta-code.factorions
! Memoize factorial function MEMO: factorial ( n -- n! ) [ 1 ] [ [1,b] product ] if-zero ;
- factorion? ( n base -- ? )
dupd >base string>digits [ factorial ] map-sum = ;
- show-factorions ( limit base -- )
dup "The factorions for base %d are:\n" printf [ [1,b) ] dip [ dupd factorion? [ pprint bl ] [ drop ] if ] curry each nl ;
1,500,000 9 12 [a,b] [ show-factorions nl ] with each</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Fōrmulæ
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In this page you can see the program(s) related to this task and their results.
FreeBASIC
<lang freebasic>Dim As Integer fact(12), suma, d, j fact(0) = 1 For n As Integer = 1 To 11
fact(n) = fact(n-1) * n
Next n For b As Integer = 9 To 12
Print "Los factoriones para base " & b & " son: " For i As Integer = 1 To 1499999 suma = 0 j = i While j > 0 d = j Mod b suma += fact(d) j \= b Wend If suma = i Then Print i & " "; Next i Print : Print
Next b Sleep</lang>
- Output:
Los factoriones para base 9 son: 1 2 41282 Los factoriones para base 10 son: 1 2 145 40585 Los factoriones para base 11 son: 1 2 26 48 40472 Los factoriones para base 12 son: 1 2
Frink
<lang frink>factorion[n, base] := sum[map["factorial", integerDigits[n, base]]]
for base = 9 to 12 {
for n = 1 to 1_499_999 if n == factorion[n, base] println["$base\t$n"]
}</lang>
- Output:
9 1 9 2 9 41282 10 1 10 2 10 145 10 40585 11 1 11 2 11 26 11 48 11 40472 12 1 12 2
Go
<lang go>package main
import (
"fmt" "strconv"
)
func main() {
// cache factorials from 0 to 11 var fact [12]uint64 fact[0] = 1 for n := uint64(1); n < 12; n++ { fact[n] = fact[n-1] * n }
for b := 9; b <= 12; b++ { fmt.Printf("The factorions for base %d are:\n", b) for i := uint64(1); i < 1500000; i++ { digits := strconv.FormatUint(i, b) sum := uint64(0) for _, digit := range digits { if digit < 'a' { sum += fact[digit-'0'] } else { sum += fact[digit+10-'a'] } } if sum == i { fmt.Printf("%d ", i) } } fmt.Println("\n") }
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Haskell
<lang haskell>import Text.Printf (printf) import Data.List (unfoldr) import Control.Monad (guard)
factorion :: Int -> Int -> Bool factorion b n = f b n == n
where f b = sum . map (product . enumFromTo 1) . unfoldr (\x -> guard (x > 0) >> pure (x `mod` b, x `div` b))
main :: IO () main = mapM_ (uncurry (printf "Factorions for base %2d: %s\n") . (\(a, b) -> (b, result a b)))
[(3,9), (4,10), (5,11), (2,12)] where factorions b = filter (factorion b) [1..] result n = show . take n . factorions</lang>
- Output:
Factorions for base 9: [1,2,41282] Factorions for base 10: [1,2,145,40585] Factorions for base 11: [1,2,26,48,40472] Factorions for base 12: [1,2]
J
<lang J>
index=: $ #: I.@:, factorion=: 10&$: :(] = [: +/ [: ! #.^:_1)&>
FACTORIONS=: 9 0 +"1 index Q=: 9 10 11 12 factorion/ i. 1500000
NB. base, factorion expressed in bases 10, and base (,. ".@:((Num_j_,26}.Alpha_j_) {~ #.inv/)"1) FACTORIONS 9 1 1 9 2 2 9 41282 62558
10 1 1 10 2 2 10 145 145 10 40585 40585 11 1 1 11 2 2 11 26 24 11 48 44 11 40472 28453 12 1 1 12 2 2
NB. tallies of factorions in the bases (9+i.4),.+/"1 Q 9 3
10 4 11 5 12 2 </lang>
Java
<lang java> public class Factorion {
public static void main(String [] args){ System.out.println("Base 9:"); for(int i = 1; i <= 1499999; i++){ String iStri = String.valueOf(i); int multiplied = operate(iStri,9); if(multiplied == i){ System.out.print(i + "\t"); } } System.out.println("\nBase 10:"); for(int i = 1; i <= 1499999; i++){ String iStri = String.valueOf(i); int multiplied = operate(iStri,10); if(multiplied == i){ System.out.print(i + "\t"); } } System.out.println("\nBase 11:"); for(int i = 1; i <= 1499999; i++){ String iStri = String.valueOf(i); int multiplied = operate(iStri,11); if(multiplied == i){ System.out.print(i + "\t"); } } System.out.println("\nBase 12:"); for(int i = 1; i <= 1499999; i++){ String iStri = String.valueOf(i); int multiplied = operate(iStri,12); if(multiplied == i){ System.out.print(i + "\t"); } } } public static int factorialRec(int n){ int result = 1; return n == 0 ? result : result * n * factorialRec(n-1); }
public static int operate(String s, int base){ int sum = 0; String strx = fromDeci(base, Integer.parseInt(s)); for(int i = 0; i < strx.length(); i++){ if(strx.charAt(i) == 'A'){ sum += factorialRec(10); }else if(strx.charAt(i) == 'B') { sum += factorialRec(11); }else if(strx.charAt(i) == 'C') { sum += factorialRec(12); }else { sum += factorialRec(Integer.parseInt(String.valueOf(strx.charAt(i)), base)); } } return sum; } // Ln 57-71 from Geeks for Geeks @ https://www.geeksforgeeks.org/convert-base-decimal-vice-versa/ static char reVal(int num) { if (num >= 0 && num <= 9) return (char)(num + 48); else return (char)(num - 10 + 65); } static String fromDeci(int base, int num){ StringBuilder s = new StringBuilder(); while (num > 0) { s.append(reVal(num % base)); num /= base; } return new String(new StringBuilder(s).reverse()); }
} </lang>
- Output:
Base 9: 1 2 41282 Base 10: 1 2 145 40585 Base 11: 1 2 26 48 40472 Base 12: 1 2
Julia
<lang julia>isfactorian(n, base) = mapreduce(factorial, +, map(c -> parse(Int, c, base=16), split(string(n, base=base), ""))) == n
printallfactorian(base) = println("Factorians for base $base: ", [n for n in 1:100000 if isfactorian(n, base)])
foreach(printallfactorian, 9:12)
</lang>
- Output:
Factorians for base 9: [1, 2, 41282] Factorians for base 10: [1, 2, 145, 40585] Factorians for base 11: [1, 2, 26, 48, 40472] Factorians for base 12: [1, 2]
Mathematica / Wolfram Language
<lang Mathematica>ClearAll[FactorionQ] FactorionQ[n_,b_:10]:=Total[IntegerDigits[n,b]!]==n Select[Range[1500000],FactorionQ[#,9]&] Select[Range[1500000],FactorionQ[#,10]&] Select[Range[1500000],FactorionQ[#,11]&] Select[Range[1500000],FactorionQ[#,12]&]</lang>
- Output:
{1, 2, 41282} {1, 2, 145, 40585} {1, 2, 26, 48, 40472} {1, 2}
Nim
Note that the library has precomputed the values of factorial, so there is no need for caching. <lang Nim>from math import fac from strutils import join
iterator digits(n, base: Natural): Natural =
## Yield the digits of "n" in base "base". var n = n while true: yield n mod base n = n div base if n == 0: break
func isFactorion(n, base: Natural): bool =
## Return true if "n" is a factorion for base "base". var s = 0 for d in n.digits(base): inc s, fac(d) result = s == n
func factorions(base, limit: Natural): seq[Natural] =
## Return the list of factorions for base "base" up to "limit". for n in 1..limit: if n.isFactorion(base): result.add(n)
for base in 9..12:
echo "Factorions for base ", base, ':' echo factorions(base, 1_500_000 - 1).join(" ")</lang>
- Output:
Factorions for base 9: 1 2 41282 Factorions for base 10: 1 2 145 40585 Factorions for base 11: 1 2 26 48 40472 Factorions for base 12: 1 2
OCaml
<lang ocaml>let () =
(* cache factorials from 0 to 11 *) let fact = Array.make 12 0 in fact.(0) <- 1; for n = 1 to pred 12 do fact.(n) <- fact.(n-1) * n; done;
for b = 9 to 12 do Printf.printf "The factorions for base %d are:\n" b; for i = 1 to pred 1_500_000 do let sum = ref 0 in let j = ref i in while !j > 0 do let d = !j mod b in sum := !sum + fact.(d); j := !j / b; done; if !sum = i then (print_int i; print_string " ") done; print_string "\n\n"; done</lang>
Pascal
modified munchhausen numbers#Pascal. output in base and 0! == 1!, so in Base 10 40585 has the same digits as 14558. <lang pascal>program munchhausennumber; {$IFDEF FPC}{$MODE objFPC}{$Optimization,On,all}{$ELSE}{$APPTYPE CONSOLE}{$ENDIF} uses
sysutils;
type
tdigit = byte;
const
MAXBASE = 17;
var
DgtPotDgt : array[0..MAXBASE-1] of NativeUint; dgtCnt : array[0..MAXBASE-1] of NativeInt; cnt: NativeUint;
function convertToString(n:NativeUint;base:byte):AnsiString; const
cBASEDIGITS = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvxyz';
var
r,dgt: NativeUint;
begin
IF base > length(cBASEDIGITS) then EXIT('Base to big'); result := ; repeat r := n div base; dgt := n-r*base; result := cBASEDIGITS[dgt+1]+result; n := r; until n =0;
end;
function CheckSameDigits(n1,n2,base:NativeUInt):boolean; var
i : NativeUInt;
Begin
fillchar(dgtCnt,SizeOf(dgtCnt),#0); repeat //increment digit of n1 i := n1;n1 := n1 div base;i := i-n1*base;inc(dgtCnt[i]); //decrement digit of n2 i := n2;n2 := n2 div base;i := i-n2*base;dec(dgtCnt[i]); until (n1=0) AND (n2= 0); result := true; For i := 2 to Base-1 do result := result AND (dgtCnt[i]=0); result := result AND (dgtCnt[0]+dgtCnt[1]=0);
end;
procedure Munch(number,DgtPowSum,minDigit:NativeUInt;digits,base:NativeInt); var
i: NativeUint; s1,s2: AnsiString;
begin
inc(cnt); number := number*base; IF digits > 1 then Begin For i := minDigit to base-1 do Munch(number+i,DgtPowSum+DgtPotDgt[i],i,digits-1,base); end else For i := minDigit to base-1 do //number is always the arrangement of the digits leading to smallest number IF (number+i)<= (DgtPowSum+DgtPotDgt[i]) then IF CheckSameDigits(number+i,DgtPowSum+DgtPotDgt[i],base) then iF number+i>0 then begin s1 := convertToString(DgtPowSum+DgtPotDgt[i],base); s2 := convertToString(number+i,base); If length(s1)= length(s2) then writeln(Format('%*d %*s %*s',[Base-1,DgtPowSum+DgtPotDgt[i],Base-1,s1,Base-1,s2])); end;
end;
//factorions procedure InitDgtPotDgt(base:byte); var
i: NativeUint;
Begin
DgtPotDgt[0]:= 1; For i := 1 to Base-1 do DgtPotDgt[i] := DgtPotDgt[i-1]*i; DgtPotDgt[0]:= 0;
end; { //Munchhausen numbers procedure InitDgtPotDgt; var
i,k,dgtpow: NativeUint;
Begin
// digit ^ digit ,special case 0^0 here 0 DgtPotDgt[0]:= 0; For i := 1 to Base-1 do Begin dgtpow := i; For k := 2 to i do dgtpow := dgtpow*i; DgtPotDgt[i] := dgtpow; end;
end; } var
base : byte;
begin
cnt := 0; For base := 2 to MAXBASE do begin writeln('Base = ',base); InitDgtPotDgt(base); Munch(0,0,0,base,base); end; writeln('Check Count ',cnt);
end.</lang>
- Output:
TIO.RUN Real time: 45.701 s User time: 44.968 s Sys. time: 0.055 s CPU share: 98.51 % Base = 2 1 1 1 Base = 3 1 1 1 2 2 2 Base = 4 1 1 1 2 2 2 7 13 13 Base = 5 1 1 1 2 2 2 49 144 144 Base = 6 1 1 1 2 2 2 25 41 14 26 42 24 Base = 7 1 1 1 2 2 2 Base = 8 1 1 1 2 2 2 Base = 9 1 1 1 2 2 2 41282 62558 25568 Base = 10 1 1 1 2 2 2 145 145 145 40585 40585 14558 Base = 11 1 1 1 2 2 2 26 24 24 48 44 44 40472 28453 23458 Base = 12 1 1 1 2 2 2 Base = 13 1 1 1 2 2 2 519326767 83790C5B 135789BC Base = 14 1 1 1 2 2 2 12973363226 8B0DD409C 11489BCDD Base = 15 1 1 1 2 2 2 1441 661 166 1442 662 266 Base = 16 1 1 1 2 2 2 2615428934649 260F3B66BF9 1236669BBFF Base = 17 1 1 1 2 2 2 40465 8405 1458 43153254185213 146F2G8500G4 111244568FGG 43153254226251 146F2G8586G4 124456688FGG Check Count 1571990934
Perl
<lang perl>use strict; use warnings; use ntheory qw/factorial todigits/;
my $limit = 1500000;
for my $b (9 .. 12) {
print "Factorions in base $b:\n"; $_ == factorial($_) and print "$_ " for 0..$b-1;
for my $i (1 .. int $limit/$b) { my $sum; my $prod = $i * $b;
for (reverse todigits($i, $b)) { $sum += factorial($_); $sum = 0 && last if $sum > $prod; }
next if $sum == 0; ($sum + factorial($_) == $prod + $_) and print $prod+$_ . ' ' for 0..$b-1; } print "\n\n";
}</lang>
- Output:
Factorions in base 9: 1 2 41282 Factorions in base 10: 1 2 145 40585 Factorions in base 11: 1 2 26 48 40472 Factorions in base 12: 1 2
Alternatively, a more efficient approach:
<lang perl>use 5.020; use ntheory qw(:all); use experimental qw(signatures); use Algorithm::Combinatorics qw(combinations_with_repetition);
sub max_power ($base = 10) {
my $m = 1; my $f = factorial($base - 1); while ($m * $f >= $base**($m-1)) { $m += 1; } return $m-1;
}
sub factorions ($base = 10) {
my @result; my @digits = (0 .. $base-1); my @factorial = map { factorial($_) } @digits;
foreach my $k (1 .. max_power($base)) { my $iter = combinations_with_repetition(\@digits, $k); while (my $comb = $iter->next) { my $n = vecsum(map { $factorial[$_] } @$comb); if (join(' ', sort { $a <=> $b } todigits($n, $base)) eq join(' ', @$comb)) { push @result, $n; } } }
return @result;
}
foreach my $base (2 .. 14) {
my @r = factorions($base); say "Factorions in base $base are (@r)";
}</lang>
- Output:
Factorions in base 2 are (1 2) Factorions in base 3 are (1 2) Factorions in base 4 are (1 2 7) Factorions in base 5 are (1 2 49) Factorions in base 6 are (1 2 25 26) Factorions in base 7 are (1 2) Factorions in base 8 are (1 2) Factorions in base 9 are (1 2 41282) Factorions in base 10 are (1 2 145 40585) Factorions in base 11 are (1 2 26 48 40472) Factorions in base 12 are (1 2) Factorions in base 13 are (1 2 519326767) Factorions in base 14 are (1 2 12973363226)
Phix
As per talk page (ok, and the task description), this is incorrectly using the base 10 limit for bases 9, 11, and 12.
with javascript_semantics for base=9 to 12 do printf(1,"The factorions for base %d are: ", base) for i=1 to 1499999 do atom total = 0, j = i, d while j>0 and total<=i do d = remainder(j,base) total += factorial(d) j = floor(j/base) end while if total==i then printf(1,"%d ", i) end if end for printf(1,"\n") end for
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Much faster, and using the correct limits
with javascript_semantics function max_power(integer base = 10) integer m = 1, f = factorial(base-1) while m*f >= power(base,m-1) do m += 1 end while return m-1 end function constant digits = "0123456789ab" function fcomb(sequence res, integer base, n, at=1, fsum=0, string chosen="") if length(chosen)=n then string fs = sort(sprintf("%a",{{base,fsum}})) if fs=chosen then res = append(res,sprintf("%d",fsum)) end if else for i=at to base do res = fcomb(res,base,n,i,fsum+factorial(i-1),chosen&digits[i]) end for end if return res end function function factorions(integer base = 10) sequence result = {} for k=1 to max_power(base) do result &= fcomb({},base,k) end for return result end function for base=2 to 12 do printf(1,"Base %2d factorions: %s\n",{base,join(factorions(base))}) end for
- Output:
Base 2 factorions: 1 2 Base 3 factorions: 1 2 Base 4 factorions: 1 2 7 Base 5 factorions: 1 2 49 Base 6 factorions: 1 2 25 26 Base 7 factorions: 1 2 Base 8 factorions: 1 2 Base 9 factorions: 1 2 41282 Base 10 factorions: 1 2 145 40585 Base 11 factorions: 1 2 26 48 40472 Base 12 factorions: 1 2
PureBasic
<lang PureBasic>Declare main()
If OpenConsole() : main() : Else : End 1 : EndIf Input() : End
Procedure main()
Define.i n,b,d,i,j,sum Dim fact.i(12) fact(0)=1 For n=1 To 11 : fact(n)=fact(n-1)*n : Next For b=9 To 12 PrintN("The factorions for base "+Str(b)+" are: ") For i=1 To 1500000-1 sum=0 : j=i While j>0 d=j%b : sum+fact(d) : j/b Wend If sum=i : Print(Str(i)+" ") : EndIf Next Print(~"\n\n") Next
EndProcedure</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Python
<lang Python>fact = [1] # cache factorials from 0 to 11 for n in range(1, 12):
fact.append(fact[n-1] * n)
for b in range(9, 12+1):
print(f"The factorions for base {b} are:") for i in range(1, 1500000): fact_sum = 0 j = i while j > 0: d = j % b fact_sum += fact[d] j = j//b if fact_sum == i: print(i, end=" ") print("\n")
</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Quackery
<lang Quackery> [ table ] is results ( n --> s )
4 times [ ' [ stack [ ] ] copy ' results put ]
[ results dup take rot join swap put ] is addresult ( n n --> )
[ table 9 10 11 12 ] is radix ( n --> n )
[ table 1 ] is ! ( n --> n ) 1 11 times [ i^ 1+ * dup ' ! put ] drop [ dip dup 0 temp put [ tuck /mod ! temp tally swap over 0 = until ] 2drop temp take = ] is factorion ( n n --> b )
1500000 times [ i^ 4 times [ dup i^ radix factorion if [ dup i^ addresult ] ] drop ] 4 times [ say "Factorions for base " i^ radix echo say ": " i^ results take echo cr ]</lang>
- Output:
Factorions for base 9: [ 1 2 41282 ] Factorions for base 10: [ 1 2 145 40585 ] Factorions for base 11: [ 1 2 26 48 40472 ] Factorions for base 12: [ 1 2 ]
Racket
<lang racket>#lang racket
(define fact
(curry list-ref (for/fold ([result (list 1)] #:result (reverse result)) ([x (in-range 1 20)]) (cons (* x (first result)) result))))
(for ([b (in-range 9 13)])
(printf "The factorions for base ~a are:\n" b) (for ([i (in-range 1 1500000)]) (let loop ([sum 0] [n i]) (cond [(positive? n) (loop (+ sum (fact (modulo n b))) (quotient n b))] [(= sum i) (printf "~a " i)]))) (newline))</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Raku
(formerly Perl 6)
<lang perl6>constant @factorial = 1, |[\*] 1..*;
constant $limit = 1500000;
constant $bases = 9 .. 12;
my @result;
$bases.map: -> $base {
@result[$base] = "\nFactorions in base $base:\n1 2";
sink (1 .. $limit div $base).map: -> $i { my $product = $i * $base; my $partial;
for $i.polymod($base xx *) { $partial += @factorial[$_]; last if $partial > $product }
next if $partial > $product;
my $sum;
for ^$base { last if ($sum = $partial + @factorial[$_]) > $product + $_; @result[$base] ~= " $sum" and last if $sum == $product + $_ } }
}
.say for @result[$bases];</lang>
- Output:
Factorions in base 9: 1 2 41282 Factorions in base 10: 1 2 145 40585 Factorions in base 11: 1 2 26 48 40472 Factorions in base 12: 1 2
REXX
<lang rexx>/*REXX program calculates and displays factorions in bases nine ───► twelve. */ parse arg LOb HIb lim . /*obtain optional arguments from the CL*/ if LOb== | LOb=="," then LOb= 9 /*Not specified? Then use the default.*/ if HIb== | HIb=="," then HIb= 12 /* " " " " " " */ if lim== | lim=="," then lim= 1500000 - 1 /* " " " " " " */
do fact=0 to HIb; !.fact= !(fact) /*use memoization for factorials. */ end /*fact*/
do base=LOb to HIb /*process all the required bases. */ @= 1 2 /*initialize the list (@) to 1 & 2. */ do j=3 for lim-2; $= 0 /*initialize the sum ($) to zero. */ t= j /*define the target (for the sum !'s).*/ do until t==0; d= t // base /*obtain a "digit".*/ $= $ + !.d /*add !(d) to sum.*/ t= t % base /*get a new target.*/ end /*until*/ if $==j then @= @ j /*Good factorial sum? Then add to list.*/ end /*i*/ say say 'The factorions for base ' right( base, length(HIb) ) " are: " @ end /*base*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ !: procedure; parse arg x; !=1; do j=2 to x; !=!*j; end; return ! /*factorials*/</lang>
- output when using the default inputs:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Ruby
<lang ruby> def factorion?(n, base)
n.digits(base).sum{|digit| (1..digit).inject(1, :*)} == n
end
(9..12).each do |base|
puts "Base #{base} factorions: #{(1..1_500_000).select{|n| factorion?(n, base)}.join(" ")} "
end </lang>
- Output:
Base 9 factorions: 1 2 41282 Base 10 factorions: 1 2 145 40585 Base 11 factorions: 1 2 26 48 40472 Base 12 factorions: 1 2
Scala
<lang scala>object Factorion extends App {
private def is_factorion(i: Int, b: Int): Boolean = { var sum = 0L var j = i while (j > 0) { sum += f(j % b) j /= b } sum == i }
private val f = Array.ofDim[Long](12) f(0) = 1L (1 until 12).foreach(n => f(n) = f(n - 1) * n) (9 to 12).foreach(b => { print(s"factorions for base $b:") (1 to 1500000).filter(is_factorion(_, b)).foreach(i => print(s" $i")) println })
}</lang>
Sidef
<lang ruby>func max_power(b = 10) {
var m = 1 var f = (b-1)! while (m*f >= b**(m-1)) { m += 1 } return m-1
}
func factorions(b = 10) {
var result = [] var digits = @^b var fact = digits.map { _! }
for k in (1 .. max_power(b)) { digits.combinations_with_repetition(k, {|*comb| var n = comb.sum_by { fact[_] } if (n.digits(b).sort == comb) { result << n } }) }
return result
}
for b in (2..12) {
var r = factorions(b) say "Base #{'%2d' % b} factorions: #{r}"
}</lang>
- Output:
Base 2 factorions: [1, 2] Base 3 factorions: [1, 2] Base 4 factorions: [1, 2, 7] Base 5 factorions: [1, 2, 49] Base 6 factorions: [1, 2, 25, 26] Base 7 factorions: [1, 2] Base 8 factorions: [1, 2] Base 9 factorions: [1, 2, 41282] Base 10 factorions: [1, 2, 145, 40585] Base 11 factorions: [1, 2, 26, 48, 40472] Base 12 factorions: [1, 2]
Swift
<lang swift>var fact = Array(repeating: 0, count: 12)
fact[0] = 1
for n in 1..<12 {
fact[n] = fact[n - 1] * n
}
for b in 9...12 {
print("The factorions for base \(b) are:")
for i in 1..<1500000 { var sum = 0 var j = i
while j > 0 { sum += fact[j % b] j /= b }
if sum == i { print("\(i)", terminator: " ") fflush(stdout) } }
print("\n")
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
Wren
<lang ecmascript>// cache factorials from 0 to 11 var fact = List.filled(12, 0) fact[0] = 1 for (n in 1..11) fact[n] = fact[n-1] * n
for (b in 9..12) {
System.print("The factorions for base %(b) are:") for (i in 1...1500000) { var sum = 0 var j = i while (j > 0) { var d = j % b sum = sum + fact[d] j = (j/b).floor } if (sum == i) System.write("%(i) ") } System.print("\n")
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
VBScript
<lang vb>' Factorions - VBScript - PG - 26/04/2020
Dim fact()
nn1=9 : nn2=12 lim=1499999
ReDim fact(nn2)
fact(0)=1 For i=1 To nn2 fact(i)=fact(i-1)*i Next For base=nn1 To nn2 list="" For i=1 To lim s=0 t=i Do While t<>0 d=t Mod base s=s+fact(d) t=t\base Loop If s=i Then list=list &" "& i Next Wscript.Echo "the factorions for base "& right(" "& base,2) &" are: "& list Next </lang>
- Output:
the factorions for base 9 are: 1 2 41282 the factorions for base 10 are: 1 2 145 40585 the factorions for base 11 are: 1 2 26 48 40472 the factorions for base 12 are: 1 2
zkl
<lang zkl>var facts=[0..12].pump(List,fcn(n){ (1).reduce(n,fcn(N,n){ N*n },1) }); #(1,1,2,6....) fcn factorions(base){
fs:=List(); foreach n in ([1..1_499_999]){ sum,j := 0,n; while(j){
sum+=facts[j%base]; j/=base;
} if(sum==n) fs.append(n); } fs
}</lang> <lang zkl>foreach n in ([9..12]){
println("The factorions for base %2d are: ".fmt(n),factorions(n).concat(" "));
}</lang>
- Output:
The factorions for base 9 are: 1 2 41282 The factorions for base 10 are: 1 2 145 40585 The factorions for base 11 are: 1 2 26 48 40472 The factorions for base 12 are: 1 2
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