Narcissistic decimal number

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Task
Narcissistic decimal number
You are encouraged to solve this task according to the task description, using any language you may know.

A   Narcissistic decimal number   is a non-negative integer,   ,   that is equal to the sum of the   -th   powers of each of the digits in the decimal representation of   ,   where     is the number of digits in the decimal representation of   .


Narcissistic (decimal) numbers are sometimes called   Armstrong   numbers, named after Michael F. Armstrong.
They are also known as   Plus Perfect   numbers.


An example
  •   if     is   153
  •   then   ,   (the number of decimal digits)   is   3
  •   we have   13 + 53 + 33   =   1 + 125 + 27   =   153
  •   and so   153   is a narcissistic decimal number


Task

Generate and show here the first   25   narcissistic decimal numbers.


Note:   ,   the first in the series.


See also



11l

Translation of: Python

<lang 11l>F narcissists(m)

  [Int] result
  L(digits) 0..
     V digitpowers = (0.<10).map(i -> i ^ @digits)
     L(n) Int(10 ^ (digits - 1)) .< 10 ^ digits
        V (div, digitpsum) = (n, 0)
        L div != 0
           (div, V mod) = divmod(div, 10)
           digitpsum += digitpowers[mod]
        I n == digitpsum
           result [+]= n
           I result.len == m
              R result

L(n) narcissists(25)

  print(n, end' ‘ ’)
  I (L.index + 1) % 5 == 0
     print()</lang>
Output:
0 1 2 3 4
5 6 7 8 9
153 370 371 407 1634
8208 9474 54748 92727 93084
548834 1741725 4210818 9800817 9926315

Ada

<lang Ada>with Ada.Text_IO;

procedure Narcissistic is

  function Is_Narcissistic(N: Natural) return Boolean is
     Decimals: Natural := 1;
     M: Natural := N;
     Sum: Natural := 0;
  begin
     while M >= 10 loop

M := M / 10; Decimals := Decimals + 1;

     end loop;
     M := N;
     while M >= 1 loop

Sum := Sum + (M mod 10) ** Decimals; M := M/10;

     end loop;
     return Sum=N;
  end Is_Narcissistic;
  
  Count, Current: Natural := 0;
  

begin

  while Count < 25 loop
     if Is_Narcissistic(Current) then

Ada.Text_IO.Put(Integer'Image(Current)); Count := Count + 1;

     end if;
     Current := Current + 1;
  end loop;

end Narcissistic;</lang>

Output:
 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Agena

Tested with Agena 2.9.5 Win32 <lang agena>scope

   # print the first 25 narcissistic numbers
   local power := reg( 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 );
   local count      := 0;
   local maxCount   := 25;
   local candidate  := 0;
   local prevDigits := 0;
   local digits     := 1;
   for d9 from 0 to 2 while count < maxCount do
       if d9 > 0 and digits < 9 then digits := 9 fi;
       for d8 from 0 to 9 while count < maxCount do
           if d8 > 0 and digits < 8 then digits := 8 fi;
           for d7 from 0 to 9 while count < maxCount do
               if d7 > 0 and digits < 7 then digits := 7 fi;
               for d6 from 0 to 9 while count < maxCount do
                   if d6 > 0 and digits < 6 then digits := 6 fi;
                   for d5 from 0 to 9 while count < maxCount do
                       if d5 > 0 and digits < 5 then digits := 5 fi;
                       for d4 from 0 to 9 while count < maxCount do
                           if d4 > 0 and digits < 4 then digits := 4 fi;
                           for d3 from 0 to 9 while count < maxCount do
                               if d3 > 0 and digits < 3 then digits := 3 fi;
                               for d2 from 0 to 9 while count < maxCount do
                                   if d2 > 0 and digits < 2 then digits := 2 fi;
                                   for d1 from 0 to 9 do
                                       if prevDigits <> digits then
                                           # number of digits has increased - increase the powers
                                           prevDigits := digits;
                                           for i from 2 to 9 do mul power[ i + 1 ], i od;
                                       fi;
                                       # sum the digits'th powers of the digits of candidate
                                       local sum := power[ d1 + 1 ] + power[ d2 + 1 ] + power[ d3 + 1 ]
                                                  + power[ d4 + 1 ] + power[ d5 + 1 ] + power[ d6 + 1 ]
                                                  + power[ d7 + 1 ] + power[ d8 + 1 ] + power[ d9 + 1 ]
                                                  ;
                                       if candidate = sum
                                       then
                                           # found another narcissistic decimal number
                                           io.write( " ", candidate );
                                           inc count, 1
                                       fi;
                                       inc candidate, 1
                                   od; # d1
                               od; # d2
                           od; # d3
                       od; # d4
                   od; # d5
               od; # d6
           od; # d7
       od; # d8
   od; # d9
   io.writeline()

epocs</lang>

Output:
 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

ALGOL 68

<lang algol68># find some narcissistic decimal numbers #

  1. returns TRUE if n is narcissitic, FALSE otherwise; n should be >= 0 #

PROC is narcissistic = ( INT n )BOOL:

    BEGIN
       # count the number of digits in n                                     #
       INT digits := 0;
       INT number := n;
       WHILE digits +:= 1;
             number OVERAB 10;
             number > 0
       DO SKIP OD;
       # sum the digits'th powers of the digits of n                         #
       INT sum := 0;
       number  := n;
       TO digits DO
           sum +:= ( number MOD 10 ) ^ digits;
           number OVERAB 10
       OD;
       # n is narcissistic if n = sum                                        #
       n = sum
    END # is narcissistic # ;
  1. print the first 25 narcissistic numbers #

INT count := 0; FOR n FROM 0 WHILE count < 25 DO

   IF is narcissistic( n ) THEN
       # found another narcissistic number                                   #
       print( ( " ", whole( n, 0 ) ) );
       count +:= 1
   FI

OD; print( ( newline ) )</lang>

Output:
 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

ALGOL W

Translation of: Agena

<lang algolw>begin

   % print the first 25 narcissistic numbers                                 %
   integer array  power( 0 :: 9 );
   integer count, candidate, prevDigits, digits;
   power( 0 ) := 0;
   for i := 1 until 9 do power( i ) := 1;
   count      := 0;
   candidate  := 0;
   prevDigits := 0;
   digits     := 1;
   for d9 := 0 until 2 do begin
       if d9 > 0 and digits < 9 then digits := 9;
       for d8 := 0 until 9 do begin
           if d8 > 0 and digits < 8 then digits := 8;
           for d7 := 0 until 9 do begin
               if d7 > 0 and digits < 7 then digits := 7;
               for d6 := 0 until 9 do begin
                   if d6 > 0 and digits < 6 then digits := 6;
                   for d5 := 0 until 9 do begin
                       if d5 > 0 and digits < 5 then digits := 5;
                       for d4 := 0 until 9 do begin
                           if d4 > 0 and digits < 4 then digits := 4;
                           for d3 := 0 until 9 do begin
                               if d3 > 0 and digits < 3 then digits := 3;
                               for d2 := 0 until 9 do begin
                                   if d2 > 0 and digits < 2 then digits := 2;
                                   for d1 := 0 until 9 do begin
                                       integer number, sum;
                                       if prevDigits <> digits then begin
                                           % number of digits has increased %
                                           % - increase the powers          %
                                           prevDigits := digits;
                                           for i := 2 until 9 do power( i ) := power( i ) * i;
                                       end;
                                       % sum the digits'th powers of the    %
                                       % digits of candidate                %
                                       sum := power( d1 ) + power( d2 ) + power( d3 )
                                            + power( d4 ) + power( d5 ) + power( d6 )
                                            + power( d7 ) + power( d8 ) + power( d9 )
                                            ;
                                       if candidate = sum then begin
                                           % found another narcissistic    %
                                           % decimal number                %
                                           writeon( i_w := 1, s_w := 1, candidate );
                                           count := count + 1;
                                           if count >= 25 then goto done
                                       end;
                                       candidate := candidate + 1
                                   end d1;
                               end d2;
                           end d3;
                       end d4;
                   end d5;
               end d6;
           end d7;
       end d8;
   end d9;

done:

   write()

end.</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 

APL

<lang apl> ∇r ← digitsOf n;digitList

 digitList ← ⍬

loop:→((⌊n)=0)/done

 digitList ← digitList,(⌊n|⍨10)
 n ← n÷10
 →loop

done: r ← ⊖digitList ∇

∇r ← getASN n;idx;list

 idx ← 0
 list ← 0⍴0

loop:

 →(n=⍴list)/done
 →(isArmstrongNumber idx)/add
 →next

add:

 list ← list,idx

next:

 idx ← idx+1
 →loop

done:

 r ← list

∇r ← isArmstrongNumber n;digits;nd

 digits ← digitsOf n  ⍝⍝ (⍎¨⍕n) is equivalent, but about 45% slower!!
 nd ← ≢ digits
 r ← n = +/digits * nd

     getASN 25

0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 </lang>

AppleScript

Functional

Translation of: JavaScript
Translation of: Haskell

AppleScript is a little out of its depth here, and imposes unproductively time-consuming hand-optimisation on the scripter, even with restriction of the search space (see the JavaScript and Haskell discussions).

For an algorithm which in JavaScript for Automation – the alternative idiom for osascript use on macOS – returns all 25 numbers in about 120 milliseconds, nearly 14 minutes are required in the AppleScript version (on the system here) for the full 7 digit search that finds the 25th number

(four seconds to scan the 5 digit combinations, and find the first 20, and 103 seconds to scan the six digit combinations for the first 21 narcissi).

For an imperative hand-optimisation, and a contrasting view, see the variant approach below :-)

<lang AppleScript>------------------------- NARCISSI -----------------------

-- isDaffodil :: Int -> Int -> Bool on isDaffodil(e, n)

   set ds to digitList(n)
   (e = length of ds) and (n = powerSum(e, ds))

end isDaffodil

-- digitList :: Int -> [Int] on digitList(n)

   if n > 0 then
       {n mod 10} & digitList(n div 10)
   else
       {}
   end if

end digitList

-- powerSum :: Int -> [Int] -> Int on powerSum(e, ns)

   script
       on |λ|(a, x)
           a + x ^ e
       end |λ|
   end script
   
   foldl(result, 0, ns) as integer

end powerSum

-- narcissiOfLength :: Int -> [Int] on narcissiOfLength(nDigits)

   script nthPower
       on |λ|(x)
           {x, x ^ nDigits as integer}
       end |λ|
   end script
   set powers to map(nthPower, enumFromTo(0, 9))
   
   script combn
       on digitTree(n, parents)
           if n > 0 then
               if parents ≠ {} then
                   script nextLayer
                       on |λ|(pair)
                           set {digit, intSum} to pair
                           script addPower
                               on |λ|(dp)
                                   set {d, p} to dp
                                   {d, p + intSum}
                               end |λ|
                           end script
                           
                           map(addPower, items 1 thru (digit + 1) of powers)
                       end |λ|
                   end script
                   
                   set nodes to concatMap(nextLayer, parents)
               else
                   set nodes to powers
               end if
               digitTree(n - 1, nodes)
           else
               script
                   on |λ|(pair)
                       isDaffodil(nDigits, item 2 of pair)
                   end |λ|
               end script
               
               filter(result, parents)
           end if
       end digitTree
   end script
   
   script snd
       on |λ|(ab)
           item 2 of ab
       end |λ|
   end script
   map(snd, combn's digitTree(nDigits, {}))

end narcissiOfLength



TEST -------------------------

on run

   {0} & concatMap(narcissiOfLength, enumFromTo(1, 5))
   -- 4 seconds, 20 narcissi
   
   -- {0} & concatMap(narcissiOfLength, enumFromTo(1, 6)) 
   -- 103 seconds, 21 narcissi
   
   -- {0} & concatMap(narcissiOfLength, enumFromTo(1, 7))
   -- 13.75 minutes, 25 narcissi
   

end run



GENERIC FUNCTIONS -------------------

-- concatMap :: (a -> [b]) -> [a] -> [b] on concatMap(f, xs)

   set lst to {}
   set lng to length of xs
   tell mReturn(f)
       repeat with i from 1 to lng
           set lst to (lst & |λ|(item i of xs, i, xs))
       end repeat
   end tell
   return lst

end concatMap

-- enumFromTo :: Int -> Int -> [Int] on enumFromTo(m, n)

   if n < m then
       set d to -1
   else
       set d to 1
   end if
   set lst to {}
   repeat with i from m to n by d
       set end of lst to i
   end repeat
   return lst

end enumFromTo

-- filter :: (a -> Bool) -> [a] -> [a] on filter(f, xs)

   tell mReturn(f)
       set lst to {}
       set lng to length of xs
       repeat with i from 1 to lng
           set v to item i of xs
           if |λ|(v, i, xs) then set end of lst to v
       end repeat
       return lst
   end tell

end filter

-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from 1 to lng
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldl

-- map :: (a -> b) -> [a] -> [b] on map(f, xs)

   tell mReturn(f)
       set lng to length of xs
       set lst to {}
       repeat with i from 1 to lng
           set end of lst to |λ|(item i of xs, i, xs)
       end repeat
       return lst
   end tell

end map

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn</lang>

Output:

<lang AppleScript>{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315}</lang>


Idiomatic

When corrected actually to return the 25 numbers required by the task, the JavaScript/Haskell translation above takes seven minutes fifty-three seconds on my current machine. By contrast, the code here was written from scratch in AppleScript, takes the number of results required as its parameter rather than the numbers of digits in them, and returns the 25 numbers in just under a sixth of a second. The first 41 numbers take just under four-and-a-half seconds, the first 42 twenty-seven, and the first 44 a minute thirty-seven-and-a-half. The 43rd and 44th numbers are both displayed in Script Editor's result pane as 4.33828176939137E+15, but appear to be the correct values when tested. The JavaScript/Haskell translation's problems are certainly not due to AppleScript being "a little out of its depth here", but the narcissistic decimal numbers beyond the 44th are admittedly beyond the resolution of AppleScript's number classes.

<lang applescript>(*

   Return the first q narcissistic decimal numbers
   (or as many of the q as can be represented by AppleScript number values).
  • )

on narcissisticDecimalNumbers(q)

   script o
       property output : {}
       property listOfDigits : missing value
       property m : 0 -- Digits per collection/number.
       property done : false
       
       -- Recursive subhandler. Builds lists containing m digit values while summing the digits' mth powers.
       on recurse(digitList, sumOfPowers, digitShortfall)
           -- If m digits have been obtained, compare the sum of powers's digits with the values in the list.
           -- Otherwise continue branching the recursion to derive longer lists.
           if (digitShortfall is 0) then
               -- Assign the list to a script property to allow faster references to its items (ie. incl. reference to script).
               set listOfDigits to digitList
               set temp to sumOfPowers
               set unmatched to m
               repeat until (temp = 0)
                   set sumDigit to temp mod 10
                   if (sumDigit is in digitList) then
                       repeat with d from 1 to unmatched
                           if (sumDigit = number d of my listOfDigits) then
                               set number d of my listOfDigits to missing value
                               set unmatched to unmatched - 1
                               exit repeat
                           end if
                       end repeat
                   else
                       exit repeat
                   end if
                   set temp to temp div 10
               end repeat
               -- If all the digits have been matched, the sum of powers is narcissistic.
               if (unmatched is 0) then
                   set end of my output to sumOfPowers div 1
                   -- If it's the qth find, signal the end of the process.
                   if ((count my output) = q) then set done to true
               end if
           else
               -- If fewer than m digits at this level, derive longer lists from the current one.
               -- Adding only values that are less than or equal to the last one makes each
               -- collection unique and turns up the narcissistic numbers in numerical order.
               repeat with additionalDigit from 0 to end of digitList
                   recurse(digitList & additionalDigit, sumOfPowers + additionalDigit ^ m, digitShortfall - 1)
                   if (done) then exit repeat
               end repeat
           end if
       end recurse
   end script
   
   (* Rest of main handler code. *)
   if (q > 89) then set q to 89 -- Number of narcissistic decimal integers known to exist.
   set maxM to 16 -- Maximum number of decimal digits (other than trailing zeros) in AppleScript numbers.
   tell o
       -- Begin with zero, which is narcissistic by definition and is never the only digit used in other numbers.
       if (q > 0) then set end of its output to 0
       if (q < 2) then set its done to true
       -- Initiate the recursive building and testing of collections of increasing numbers of digit values.
       repeat until (its done)
           set its m to (its m) + 1
           if (its m > maxM) then
               set end of its output to "Remaining numbers beyond AppleScript's number precision"
               set its done to true
           else
               repeat with digit from 1 to 9
                   recurse({digit}, digit ^ (its m), (its m) - 1)
                   if (its done) then exit repeat
               end repeat
           end if
       end repeat
       
       return its output
   end tell

end narcissisticDecimalNumbers

return narcissisticDecimalNumbers(25)</lang>

Output:

<lang applescript>{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315}</lang>

AutoHotkey

<lang AutoHotkey>

  1. NoEnv ; Do not try to use environment variables

SetBatchLines, -1 ; Execute as quickly as you can

StartCount := A_TickCount Narc := Narc(25) Elapsed := A_TickCount - StartCount

MsgBox, Finished in %Elapsed%ms`n%Narc% return

Narc(m) { Found := 0, Lower := 0 Progress, B2 Loop { Max := 10 ** Digits:=A_Index Loop, 10 Index := A_Index-1, Powers%Index% := Index**Digits While Lower < Max { Sum := 0 Loop, Parse, Lower Sum += Powers%A_LoopField% Loop, 10 {

if (Lower + (Index := A_Index-1) == Sum + Powers%Index%) { Out .= Lower+Index . (Mod(++Found,5) ? ", " : "`n") Progress, % Found/M*100 if (Found >= m) { Progress, Off return Out } } } Lower += 10 } } } </lang>

Output:
Finished in 17690ms
0, 1, 2, 3, 4
5, 6, 7, 8, 9
153, 370, 371, 407, 1634
8208, 9474, 54748, 92727, 93084
548834, 1741725, 4210818, 9800817, 9926315

This is a derivative of the python example, but modified for speed reasons.

Instead of summing all the powers of all the numbers at once, we sum the powers for this multiple of 10, then check each number 0 through 9 at once before summing the next multiple of 10. This way, we don't have to calculate the sum of 174172_ for every number 1741720 through 1741729.

AWK

<lang AWK>

  1. syntax: GAWK -f NARCISSISTIC_DECIMAL_NUMBER.AWK

BEGIN {

   for (n=0;;n++) {
     leng = length(n)
     sum = 0
     for (i=1; i<=leng; i++) {
       c = substr(n,i,1)
       sum += c ^ leng
     }
     if (n == sum) {
       printf("%d ",n)
       if (++count == 25) { break }
     }
   }
   exit(0)

} </lang>

output:

0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Befunge

This can take several minutes to complete in most interpreters, so it's probably best to use a compiler if you want to see the full sequence.

<lang befunge>p55*\>:>:>:55+%\55+/00gvv_@ >1>+>^v\_^#!:<p01p00:+1<>\> >#-_>\>20p110g>\20g*\v>1-v| ^!p00:-1g00+$_^#!:<-1<^\.:<</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

BQN

B10 is a BQNcrate idiom to get the digits of a number.

<lang bqn>B10 ← 10{⌽𝕗|⌊∘÷⟜𝕗⍟(↕1+·⌊𝕗⋆⁼1⌈⊢)} IsNarc ← {𝕩=+´⋆⟜≠B10 𝕩}

/IsNarc¨ ↕1e7</lang><lang bqn>⟨0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315⟩</lang>

A much faster method is to generate a list of digit sums as addition tables (+⌜). A different list of digit sums is generated for each digit count, 0 to 7. To avoid leading 0s, 0 is removed from the first digit list with (0=↕)↓¨. Then all that needs to be done is to join the lists and return locations where the index (number) and value (digit power sum) are equal.

<lang bqn>/ ↕∘≠⊸= ∾ (⥊0+⌜´(0=↕)↓¨(<↕10)⋆⊢)¨↕8</lang>

C

For a much longer but faster solution, see Narcissistic decimal number/C.

The following prints the first 25 numbers, though not in order... <lang c>#include <stdio.h>

  1. include <gmp.h>
  1. define MAX_LEN 81

mpz_t power[10]; mpz_t dsum[MAX_LEN + 1]; int cnt[10], len;

void check_perm(void) { char s[MAX_LEN + 1]; int i, c, out[10] = { 0 };

mpz_get_str(s, 10, dsum[0]); for (i = 0; s[i]; i++) { c = s[i]-'0'; if (++out[c] > cnt[c]) return; }

if (i == len) gmp_printf(" %Zd", dsum[0]); }

void narc_(int pos, int d) { if (!pos) { check_perm(); return; }

do { mpz_add(dsum[pos-1], dsum[pos], power[d]); ++cnt[d]; narc_(pos - 1, d); --cnt[d]; } while (d--); }

void narc(int n) { int i; len = n; for (i = 0; i < 10; i++) mpz_ui_pow_ui(power[i], i, n);

mpz_init_set_ui(dsum[n], 0);

printf("length %d:", n); narc_(n, 9); putchar('\n'); }

int main(void) { int i;

for (i = 0; i <= 10; i++) mpz_init(power[i]); for (i = 1; i <= MAX_LEN; i++) narc(i);

return 0; }</lang>

Output:
length 1: 9 8 7 6 5 4 3 2 1 0
length 2:
length 3: 407 371 370 153
length 4: 9474 8208 1634
length 5: 93084 92727 54748
length 6: 548834
length 7: 9926315 9800817 4210818 1741725
length 8: 88593477 24678051 24678050
length 9: 912985153 534494836 472335975 146511208
length 10: 4679307774
length 11: 94204591914 82693916578 49388550606 44708635679 42678290603 40028394225 32164049651 32164049650
length 12:
length 13:
length 14: 28116440335967
length 15:
length 16: 4338281769391371 4338281769391370
length 17: 35875699062250035 35641594208964132 21897142587612075
length 18:
^C

C#

<lang csharp> using System;

namespace Narcissistic {

   class Narcissistic
   {
       public bool isNarcissistic(int z)
       {
           if (z < 0) return false;
           string n = z.ToString();
           int t = 0, l = n.Length;
           foreach (char c in n)
               t += Convert.ToInt32(Math.Pow(Convert.ToDouble(c - 48), l));
           return t == z;
       }
   }
   class Program
   {
       static void Main(string[] args)
       {
           Narcissistic n = new Narcissistic();
           int c = 0, x = 0;
           while (c < 25)
           {
               if (n.isNarcissistic(x))
               {
                   if (c % 5 == 0) Console.WriteLine();
                   Console.Write("{0,7} ", x);
                   c++;
               }
               x++;
           }
           Console.WriteLine("\n\nPress any key to continue...");
           Console.ReadKey();
       }
   }

} </lang>

Output:
      0       1       2       3       4
      5       6       7       8       9
    153     370     371     407    1634
   8208    9474   54748   92727   93084
 548834 1741725 4210818 9800817 9926315

or

<lang csharp> //Narcissistic numbers: Nigel Galloway: February 17th., 2015 using System; using System.Collections.Generic; using System.Linq;

namespace RC {

   public static class NumberEx {
       public static IEnumerable<int> Digits(this int n) {
           List<int> digits = new List<int>();
           while (n > 0) {
               digits.Add(n % 10);
               n /= 10;
           }
           return digits.AsEnumerable();
       }
   }
   class Program {
       static void Main(string[] args) {
           foreach (int N in Enumerable.Range(0, Int32.MaxValue).Where(k => {
               var digits = k.Digits();
               return digits.Sum(x => Math.Pow(x, digits.Count())) == k;
           }).Take(25)) {
               System.Console.WriteLine(N);
           }
       }
   }

} </lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315

All 89 terms

Translation of: FreeBASIC
(FreeBASIC, GMP version)
Why stop at 25? Even using ulong instead of int only gets one to the 44th item. The 89th (last) item has 39 digits, which BigInteger easily handles. Of course, the BigInteger implementation is slower than native data types. But one can compensate a bit by calculating in parallel. Not bad, it can get all 89 items in under 7 1/2 minutes on a core i7. The calculation to the 25th item takes a fraction of a second. The calculation for all items up to 25 digits long (67th item) takes about half a minute with sequential processing and less than a quarter of a minute using parallel processing. Note that parallel execution involves some overhead, and isn't a time improvement unless computing around 15 digits or more. This program can test all numbers up to 61 digits in under half an hour, of course the highest item found has only 39 digits.

<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Threading.Tasks; using System.Numerics;

static class Program {

   public static void nar(int max, bool only1 = false)
   {
       int n, n1, n2, n3, n4, n5, n6, n7, n8, n9;
       int[] d;                                       // digits tally
       char [] bs;                                    // BigInteger String
       List<BigInteger> res = new List<BigInteger>(); // per n digits results
       BigInteger[,] p = new BigInteger[10, max + 1]; // powers array
       // BigIntegers for intermediate results
       BigInteger x2, x3, x4, x5, x6, x7, x8, x9;
       for (n = only1 ? max : 1; n <= max; n++) // main loop
       {
           for (int i = 1; i <= 9; i++) // init powers array for this n
           {
               p[i, 1] = BigInteger.Pow(i, n);
               for (int j = 2; j <= n; j++) p[i, j] = p[i, 1] * j;
           }
           for (n9 = n; n9 >= 0; n9--) // nested loops...
           {
               x9 = p[9, n9];
               for (n8 = n - n9; n8 >= 0; n8--)
               {
                   x8 = x9 + p[8, n8];
                   for (n7 = n - n9 - n8; n7 >= 0; n7--)
                   {
                       x7 = x8 + p[7, n7];
                       for (n6 = n - n9 - n8 - n7; n6 >= 0; n6--)
                       {
                           x6 = x7 + p[6, n6];
                           for (n5 = n - n9 - n8 - n7 - n6; n5 >= 0; n5--)
                           {
                               x5 = x6 + p[5, n5];
                               for (n4 = n - n9 - n8 - n7 - n6 - n5; n4 >= 0; n4--)
                               {
                                   x4 = x5 + p[4, n4];
                                   for (n3 = n - n9 - n8 - n7 - n6 - n5 - n4; n3 >= 0; n3--)
                                   {
                                       x3 = x4 + p[3, n3];
                                       for (n2 = n - n9 - n8 - n7 - n6 - n5 - n4 - n3; n2 >= 0; n2--)
                                       {
                                           x2 = x3 + p[2, n2];
                                           for (n1 = n - n9 - n8 - n7 - n6 - n5 - n4 - n3 - n2; n1 >= 0; n1--)
                                           {
                                               bs = (x2 + n1).ToString().ToCharArray();
                                               switch (bs.Length.CompareTo(n))
                                               { // Since all the for/next loops step down, when the digit count
                                                 // becomes smaller than n, it's time to try the next n value.
                                                   case -1: { goto Next_n; }
                                                   case 0:
                                                       {
                                                           d = new int[10]; foreach (char c in bs) d[c - 48] += 1;
                                                           if (n9 == d[9] && n8 == d[8] && n7 == d[7] && 
                                                               n6 == d[6] && n5 == d[5] && n4 == d[4] && 
                                                               n3 == d[3] && n2 == d[2] && n1 == d[1] && 
                                                               n - n9 - n8 - n7 - n6 - n5 - n4 - n3 - n2 - n1 == d[0])
                                                               res.Add(BigInteger.Parse(new string(bs)));
                                                           break;
                                                       }
                                               }
                                           }
                                       }
                                   }
                               }
                           }
                       }
                   }
               }
           }

Next_n: if (only1) {

               Console.Write("{0} ", n); lock (resu) resu.AddRange(res); return;
           } else {
               res.Sort(); Console.WriteLine("{2,3} {0,3}: {1}", 
               Math.Ceiling((DateTime.Now - st).TotalSeconds), string.Join(" ", res), n); res.Clear();
           }
       }
   }
   private static DateTime st = default(DateTime);
   private static List<BigInteger> resu = new List<BigInteger>();
   private static bool para = true; // parallel (default) or sequential calcualtion
   private static int lim = 7;  // this is the number of digits to calcualate, not the nth entry.
                                // for up to the 25th item, use lim = 7 digits.
                                // for all 89 items, use lim = 39 digits.
   public static void Main(string[] args)
   {
       if (args.Count() > 0)
       {
           int t = lim; int.TryParse(args[0], out t);
           if (t < 1) t = 1;   // number of digits must be > 0
           if (t > 61) t = 61; // no point when lim * math.pow(9, lim) < math.pow(10, lim - 1)
           lim = t;
           // default is parallel, will do sequential when any 2nd command line parameter is present.
           para = !(args.Count() > 1);
       }
       st = DateTime.Now;
       if (para)
       {
           Console.Write("Calculations in parallel... "); // starts the bigger ones first
           Parallel.ForEach(Enumerable.Range(1, lim).Reverse().ToArray(), n => { nar(n, true); } );
           resu.Sort(); int[] g = Enumerable.Range(1, resu.Count).ToArray();
           var both = g.Zip(resu, (a, b) => a.ToString() + " " + b.ToString());
           Console.WriteLine("\n{0}", string.Join("\n", both));
       }
       else { Console.WriteLine("Sequential calculations:"); nar(lim); }
       Console.WriteLine("Total elasped: {0} seconds", (DateTime.Now - st).TotalSeconds);
       if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
   }

} </lang>

Output:
(with command line parameter = "39")
Calculations in parallel... 7 6 5 4 3 2 1 11 10 9 8 15 14 13 12 19 18 17 16 23 22 20 21 26 27 25 24 30 31 29 34 28 35 38 33 39 32 37 36
1 0
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
11 153
12 370
13 371
14 407
15 1634
16 8208
17 9474
18 54748
19 92727
20 93084
21 548834
22 1741725
23 4210818
24 9800817
25 9926315
26 24678050
27 24678051
28 88593477
29 146511208
30 472335975
31 534494836
32 912985153
33 4679307774
34 32164049650
35 32164049651
36 40028394225
37 42678290603
38 44708635679
39 49388550606
40 82693916578
41 94204591914
42 28116440335967
43 4338281769391370
44 4338281769391371
45 21897142587612075
46 35641594208964132
47 35875699062250035
48 1517841543307505039
49 3289582984443187032
50 4498128791164624869
51 4929273885928088826
52 63105425988599693916
53 128468643043731391252
54 449177399146038697307
55 21887696841122916288858
56 27879694893054074471405
57 27907865009977052567814
58 28361281321319229463398
59 35452590104031691935943
60 174088005938065293023722
61 188451485447897896036875
62 239313664430041569350093
63 1550475334214501539088894
64 1553242162893771850669378
65 3706907995955475988644380
66 3706907995955475988644381
67 4422095118095899619457938
68 121204998563613372405438066
69 121270696006801314328439376
70 128851796696487777842012787
71 174650464499531377631639254
72 177265453171792792366489765
73 14607640612971980372614873089
74 19008174136254279995012734740
75 19008174136254279995012734741
76 23866716435523975980390369295
77 1145037275765491025924292050346
78 1927890457142960697580636236639
79 2309092682616190307509695338915
80 17333509997782249308725103962772
81 186709961001538790100634132976990
82 186709961001538790100634132976991
83 1122763285329372541592822900204593
84 12639369517103790328947807201478392
85 12679937780272278566303885594196922
86 1219167219625434121569735803609966019
87 12815792078366059955099770545296129367
88 115132219018763992565095597973971522400
89 115132219018763992565095597973971522401
Total elasped: 443.8791684 seconds

(without any command line parameters)

Calculations in parallel... 1 3 2 4 5 7 6
1 0
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
11 153
12 370
13 371
14 407
15 1634
16 8208
17 9474
18 54748
19 92727
20 93084
21 548834
22 1741725
23 4210818
24 9800817
25 9926315
Total elasped: 0.0279259 seconds

(with command line parameters= "7 x")

Sequential calculations:
  1   1: 0 1 2 3 4 5 6 7 8 9
  2   1:
  3   1: 153 370 371 407
  4   1: 1634 8208 9474
  5   1: 54748 92727 93084
  6   1: 548834
  7   1: 1741725 4210818 9800817 9926315
Total elasped: 0.0175957 seconds


(with command line parameters= "25 x")

Sequential calculations:
  1   1: 0 1 2 3 4 5 6 7 8 9
  2   1:
  3   1: 153 370 371 407
  4   1: 1634 8208 9474
  5   1: 54748 92727 93084
  6   1: 548834
  7   1: 1741725 4210818 9800817 9926315
  8   1: 24678050 24678051 88593477
  9   1: 146511208 472335975 534494836 912985153
 10   1: 4679307774
 11   1: 32164049650 32164049651 40028394225 42678290603 44708635679 49388550606 82693916578 94204591914
 12   1:
 13   1:
 14   1: 28116440335967
 15   1:
 16   1: 4338281769391370 4338281769391371
 17   2: 21897142587612075 35641594208964132 35875699062250035
 18   3:
 19   4: 1517841543307505039 3289582984443187032 4498128791164624869 4929273885928088826
 20   6: 63105425988599693916
 21   9: 128468643043731391252 449177399146038697307
 22  12:
 23  17: 21887696841122916288858 27879694893054074471405 27907865009977052567814 28361281321319229463398 35452590104031691935943
 24  23: 174088005938065293023722 188451485447897896036875 239313664430041569350093
 25  31: 1550475334214501539088894 1553242162893771850669378 3706907995955475988644380 3706907995955475988644381 4422095118095899619457938
Total elasped: 30.5658944 seconds

C++

<lang cpp>

  1. include <iostream>
  2. include <vector>

using namespace std; typedef unsigned int uint;

class NarcissisticDecs { public:

   void makeList( int mx )
   {

uint st = 0, tl; int pwr = 0, len;

       while( narc.size() < mx )

{ len = getDigs( st ); if( pwr != len ) { pwr = len; fillPower( pwr ); }

           tl = 0;

for( int i = 1; i < 10; i++ ) tl += static_cast<uint>( powr[i] * digs[i] );

if( tl == st ) narc.push_back( st ); st++; }

   }
   void display()
   {

for( vector<uint>::iterator i = narc.begin(); i != narc.end(); i++ ) cout << *i << " "; cout << "\n\n";

   }

private:

   int getDigs( uint st )
   {

memset( digs, 0, 10 * sizeof( int ) ); int r = 0; while( st ) { digs[st % 10]++; st /= 10; r++; }

       return r;
   }
   void fillPower( int z )
   {

for( int i = 1; i < 10; i++ ) powr[i] = pow( static_cast<float>( i ), z );

   }
   vector<uint> narc;
   uint powr[10];
   int digs[10];

};

int main( int argc, char* argv[] ) {

   NarcissisticDecs n;
   n.makeList( 25 );
   n.display();
   return system( "pause" );

} </lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Clojure

Find N first Narcissistic numbers. <lang Clojure> (ns narcissistic.core

 (:require [clojure.math.numeric-tower :as math]))

(defn digits [n] ;; digits of a number.

 (->> n str (map (comp read-string str))))

(defn narcissistic? [n] ;; True if the number is a Narcissistic one.

 (let [d (digits n)
       s (count d)]
   (= n (reduce + (map #(math/expt % s) d)))))

(defn firstNnarc [n] ;;list of the first "n" Narcissistic numbers.

 (take n (filter narcissistic? (range))))

</lang>

Output:

by Average-user

(time (doall (firstNnarc 25)))
"Elapsed time: 186430.429966 msecs"
(0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315)

COBOL

<lang COBOL>

      PROGRAM-ID. NARCISSIST-NUMS.
      DATA DIVISION.
      WORKING-STORAGE SECTION.

          01 num-length PIC 9(2) value 0.
          01 in-sum PIC  9(9) value 0.
          01 counter PIC  9(9) value 0.
          01 current-number PIC  9(9) value 0.
          01 narcissist PIC Z(9).
          01 temp PIC  9(9) value 0.
          01 modulo PIC  9(9) value 0.
          01 answer PIC  9 .

      PROCEDURE DIVISION.
      MAIN-PROCEDURE.
          DISPLAY "the first 20 narcissist numbers:" .

          MOVE 20 TO counter.
          PERFORM UNTIL counter=0

              PERFORM 000-NARCISSIST-PARA

                  IF answer = 1 
                      SUBTRACT 1 from counter
                      GIVING counter
                      MOVE current-number TO narcissist
                      DISPLAY narcissist
                  END-IF

                  ADD 1 TO current-number

              END-PERFORM

           STOP RUN.

      000-NARCISSIST-PARA.

            MOVE ZERO TO in-sum.
            MOVE current-number TO temp.
            COMPUTE num-length =1+  FUNCTION Log10(temp)

            PERFORM  UNTIL temp=0

                 DIVIDE temp BY 10 GIVING temp
                           REMAINDER  modulo

                 COMPUTE modulo=modulo**num-length
                 ADD modulo to in-sum GIVING in-sum

           END-PERFORM.

              IF current-number=in-sum
                  MOVE 1 TO answer
                  ELSE MOVE 0 TO answer
              END-IF.

      END PROGRAM NARCISSIST-NUMS.
      

</lang>

Output:
the first 20 narcissist numbers:
        0
        1
        2
        3
        4
        5
        6
        7
        8
        9
      153
      370
      371
      407
     1634
     8208
     9474
    54748
    92727
    93084

Common Lisp

<lang lisp> (defun integer-to-list (n)

 (map 'list #'digit-char-p (prin1-to-string n)))

(defun narcissisticp (n)

 (let* ((lst (integer-to-list n))
        (e (length lst)))
       (= n

(reduce #'+ (mapcar (lambda (x) (expt x e)) lst)))))

(defun start ()

 (loop for c from 0
       while (< narcissistic 25)
       counting (narcissisticp c) into narcissistic
       do (if (narcissisticp c) (print c))))

</lang>

Output:
CL-USER> (start)

0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
153 
370 
371 
407 
1634 
8208 
9474 
54748 
92727 
93084 
548834 
1741725 
4210818 
9800817 
9926315 
NIL

D

Simple Version

<lang d>void main() {

   import std.stdio, std.algorithm, std.conv, std.range;
   immutable isNarcissistic = (in uint n) pure @safe =>
       n.text.map!(d => (d - '0') ^^ n.text.length).sum == n;
   writefln("%(%(%d %)\n%)",
            uint.max.iota.filter!isNarcissistic.take(25).chunks(5));

}</lang>

Output:
0 1 2 3 4
5 6 7 8 9
153 370 371 407 1634
8208 9474 54748 92727 93084
548834 1741725 4210818 9800817 9926315

Fast Version

Translation of: Python

<lang d>import std.stdio, std.algorithm, std.range, std.array;

uint[] narcissists(in uint m) pure nothrow @safe {

   typeof(return) result;
   foreach (immutable uint digits; 0 .. 10) {
       const digitPowers = 10.iota.map!(i => i ^^ digits).array;
       foreach (immutable uint n; 10 ^^ (digits - 1) .. 10 ^^ digits) {
           uint digitPSum, div = n;
           while (div) {
               digitPSum += digitPowers[div % 10];
               div /= 10;
           }
           if (n == digitPSum) {
               result ~= n;
               if (result.length >= m)
                   return result;
           }
       }
   }
   assert(0);

}

void main() {

   writefln("%(%(%d %)\n%)", 25.narcissists.chunks(5));

}</lang> With LDC2 compiler prints the same output in less than 0.3 seconds.

Faster Version

Translation of: C

<lang d>import std.stdio, std.bigint, std.conv;

struct Narcissistics(TNum, uint maxLen) {

   TNum[10] power;
   TNum[maxLen + 1] dsum;
   uint[10] count;
   uint len;
   void checkPerm() const {
       uint[10] mout;
       immutable s = dsum[0].text;
       foreach (immutable d; s) {
           immutable c = d - '0';
           if (++mout[c] > count[c])
               return;
       }
       if (s.length == len)
           writef(" %d", dsum[0]);
   }
   void narc2(in uint pos, uint d) {
       if (!pos) {
           checkPerm;
           return;
       }
       do {
           dsum[pos - 1] = dsum[pos] + power[d];
           count[d]++;
           narc2(pos - 1, d);
           count[d]--;
       } while (d--);
   }
   void show(in uint n) {
       len = n;
       foreach (immutable i, ref p; power)
           p = TNum(i) ^^ n;
       dsum[n] = 0;
       writef("length %d:", n);
       narc2(n, 9);
       writeln;
   }

}

void main() {

   enum maxLength = 16;
   Narcissistics!(ulong, maxLength) narc;
   //Narcissistics!(BigInt, maxLength) narc; // For larger numbers.
   foreach (immutable i; 1 .. maxLength + 1)
       narc.show(i);

}</lang>

Output:
length 1: 9 8 7 6 5 4 3 2 1 0
length 2:
length 3: 407 371 370 153
length 4: 9474 8208 1634
length 5: 93084 92727 54748
length 6: 548834
length 7: 9926315 9800817 4210818 1741725
length 8: 88593477 24678051 24678050
length 9: 912985153 534494836 472335975 146511208
length 10: 4679307774
length 11: 94204591914 82693916578 49388550606 44708635679 42678290603 40028394225 32164049651 32164049650
length 12:
length 13:
length 14: 28116440335967
length 15:
length 16: 4338281769391371 4338281769391370

With LDC2 compiler and maxLength=16 the run-time is about 0.64 seconds.

Elixir

Translation of: D

<lang elixir>defmodule RC do

 def narcissistic(m) do
   Enum.reduce(1..10, [0], fn digits,acc ->
     digitPowers = List.to_tuple(for i <- 0..9, do: power(i, digits))
     Enum.reduce(power(10, digits-1) .. power(10, digits)-1, acc, fn n,result ->
       sum = divsum(n, digitPowers, 0)
       if n == sum do
         if length(result) == m-1, do: throw Enum.reverse(result, [n])
         [n | result]
       else
         result
       end
     end)
   end)
 end
 
 defp divsum(0, _, sum), do: sum
 defp divsum(n, digitPowers, sum) do
   divsum(div(n,10), digitPowers, sum+elem(digitPowers,rem(n,10)))
 end
 
 defp power(n, m), do: power(n, m, 1)
 
 defp power(_, 0, pow), do: pow
 defp power(n, m, pow), do: power(n, m-1, pow*n)

end

try do

 RC.narcissistic(25)

catch

 x -> IO.inspect x

end</lang>

Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748,
 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315]

ERRE

<lang ERRE>PROGRAM NARCISISTIC

!$DOUBLE

BEGIN

   N=0
   LOOP
     C$=MID$(STR$(N),2)
     LENG=LEN(C$)
     SUM=0
     FOR I=1 TO LENG DO
       C=VAL(MID$(C$,I,1))
       SUM+=C^LENG
     END FOR
     IF N=SUM THEN
       PRINT(N;)
       COUNT=COUNT+1
       EXIT IF COUNT=25
     END IF
     N=N+1
   END LOOP

END PROGRAM</lang> Output

 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834
 1741725 4210818  9800817 9926315

F#

<lang fsharp> //Naïve solution of Narcissitic number: Nigel Galloway - Febryary 18th., 2015 open System let rec _Digits (n,g) = if n < 10 then n::g else _Digits(n/10,n%10::g)

seq{0 .. Int32.MaxValue} |> Seq.filter (fun n ->

 let d = _Digits (n, [])
 d |> List.fold (fun a l -> a + int ((float l) ** (float (List.length d)))) 0 = n) |> Seq.take(25) |> Seq.iter (printfn "%A")

</lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315

Factor

<lang>USING: io kernel lists lists.lazy math math.functions math.text.utils prettyprint sequences ; IN: rosetta-code.narcissistic-decimal-number

digit-count ( n -- count ) log10 floor >integer 1 + ;
narcissist? ( n -- ? ) dup [ 1 digit-groups ]
   [ digit-count [ ^ ] curry ] bi map-sum = ;
   
first25 ( -- seq ) 25 0 lfrom [ narcissist? ] lfilter
   ltake list>array ;
   
main ( -- ) first25 [ pprint bl ] each ;

MAIN: main</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Forth

Works with: GNU Forth version 0.7.0

<lang forth>

: dig.num                           \ returns input number and the number of its digits ( n -- n n1 )

dup 0 swap

    begin

swap 1 + swap dup 10 >= while 10 /

    repeat

drop ;

: zero.divmod                         \ /mod that returns zero if number is zero

dup 0 = if drop 0 else

          /mod 

then ;

: zero.div                            \ division that returns zero if divisor is zero

dup 0 = if drop else

        /

then ;

: next.last

depth 2 - roll ; \ gets next-to-last number from the stack

: ten.to			          \ ( n -- 10^n ) returns 1 for zero and negative

dup 0 <= if drop 1 else dup 1 = if drop 10 else 10 swap 1 do 10 * loop then then ;

: split.div                                        \ returns input number and its digits ( n -- n n1 n2 n3....)

dup 10 < if dup else \ duplicates single digit numbers dig.num \ provides number of digits swap dup rot dup 1 - ten.to swap \ stack juggling, ten raised to number of digits - 1... 1 do \ ... is the needed divisor, counter on top and ... dup rot swap zero.divmod swap rot 10 / \ ...division loop loop drop then ;

: to.pow                           \ nth power of positive numbers ( n m -- n^m )

swap dup rot dup 0 <= if 2drop drop 1 else 0 do swap dup rot * loop swap zero.div then ;

: num.pow                        \ raises each digit to the power of (number of digits) 

depth 1 - 0 do next.last depth 1 - to.pow loop ;

: add.num 

depth 2 > if begin + depth 2 = until then ;

: narc.check

split.div

       num.pow 
       add.num ;
: narc.num 0 { a b }              \  ( m -- n1 n2 n3 ... nm )

page \ displays m narcissistic decimal numbers... 999999999 0 do \ ...beginning with 0 a b = if leave then i narc.check = if i . cr b 1 + to b then loop  ;

25 narc.num

</lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315
 ok

FreeBASIC

Simple Version

<lang FreeBASIC>' normal version: 14-03-2017 ' compile with: fbc -s console ' can go up to 18 digits (ulongint is 64bit), above 18 overflow will occur

Dim As Integer n, n0, n1, n2, n3, n4, n5, n6, n7, n8, n9, a, b Dim As Integer d() Dim As ULongInt d2pow(0 To 9) = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} Dim As ULongInt x Dim As String str_x

For n = 1 To 7

 For n9 = n To 0 Step -1
   For n8 = n-n9 To 0 Step -1
     For n7 = n-n9-n8 To 0 Step -1
       For n6 = n-n9-n8-n7 To 0 Step -1
         For n5 = n-n9-n8-n7-n6 To 0 Step -1
           For n4 = n-n9-n8-n7-n6-n5 To 0 Step -1
             For n3 = n-n9-n8-n7-n6-n5-n4 To 0 Step -1
               For n2 = n-n9-n8-n7-n6-n5-n4-n3 To 0 Step -1
                 For n1 = n-n9-n8-n7-n6-n5-n4-n3-n2 To 0 Step -1
                   n0 = n-n9-n8-n7-n6-n5-n4-n3-n2-n1

                   x = n1 + n2*d2pow(2) + n3*d2pow(3) + n4*d2pow(4) + n5*d2pow(5)_
                          + n6*d2pow(6) + n7*d2pow(7) + n8*d2pow(8) + n9*d2pow(9)

                   str_x = Str(x)
                   If Len(str_x) = n Then

                     ReDim d(10)
                     For a = 0 To n-1
                       d(Str_x[a]- Asc("0")) += 1
                     Next a

                     If n0 = d(0) AndAlso n1 = d(1) AndAlso n2 = d(2) AndAlso n3 = d(3)_
                                  AndAlso n4 = d(4) AndAlso n5 = d(5) AndAlso n6 = d(6)_
                                  AndAlso n7 = d(7) AndAlso n8 = d(8) AndAlso n9 = d(9) Then
                       Print x
                     End If
                   End If

                 Next n1
               Next n2
             Next n3
           Next n4
         Next n5
       Next n6
     Next n7
   Next n8
 Next n9

 For a As Integer = 2 To 9
   d2pow(a) = d2pow(a) * a
 Next a

Next n

' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang>

Output:
9
8
7
6
5
4
3
2
1
0
407
371
370
153
9474
8208
1634
93084
92727
54748
548834
9926315
9800817
4210818
1741725

GMP Version

It takes about 35 min. to find all 88 numbers (39 digits).
To go all the way it takes about 2 hours.

<lang FreeBASIC>' gmp version: 17-06-2015 ' uses gmp ' compile with: fbc -s console

  1. Include Once "gmp.bi"

' change the number after max for the maximum n-digits you want (2 to 61)

  1. Define max 61

Dim As Integer n, n0, n1, n2, n3, n4, n5, n6, n7, n8, n9 Dim As Integer i, j Dim As UInteger d() Dim As ZString Ptr gmp_str gmp_str = Allocate(100)

' create gmp integer array, Dim d2pow(9, max) As Mpz_ptr ' initialize array and set start value, For i = 0 To 9

 For j = 0 To max
   d2pow(i, j) = Allocate(Len(__mpz_struct)) : Mpz_init(d2pow(i, j))
 Next j

Next i

' gmp integers for to hold intermediate result Dim As Mpz_ptr x1 = Allocate(Len(__mpz_struct)) : Mpz_init(x1) Dim As Mpz_ptr x2 = Allocate(Len(__mpz_struct)) : Mpz_init(x2) Dim As Mpz_ptr x3 = Allocate(Len(__mpz_struct)) : Mpz_init(x3) Dim As Mpz_ptr x4 = Allocate(Len(__mpz_struct)) : Mpz_init(x4) Dim As Mpz_ptr x5 = Allocate(Len(__mpz_struct)) : Mpz_init(x5) Dim As Mpz_ptr x6 = Allocate(Len(__mpz_struct)) : Mpz_init(x6) Dim As Mpz_ptr x7 = Allocate(Len(__mpz_struct)) : Mpz_init(x7) Dim As Mpz_ptr x8 = Allocate(Len(__mpz_struct)) : Mpz_init(x8)

For n = 1 To max

 For i = 1 To 9
   'Mpz_set_ui(d2pow(i,0), 0)
   Mpz_ui_pow_ui(d2pow(i,1), i, n)
   For j = 2 To n
     Mpz_mul_ui(d2pow(i, j), d2pow(i, 1), j)
   Next j
 Next i
 For n9 = n To 0 Step -1
   For n8 = n-n9 To 0 Step -1
     Mpz_add(x8, d2pow(9, n9), d2pow(8, n8))
     For n7 = n-n9-n8 To 0 Step -1
       Mpz_add(x7, x8, d2pow(7, n7))
       For n6 = n-n9-n8-n7 To 0 Step -1
         Mpz_add(x6, x7, d2pow(6, n6))
         For n5 = n-n9-n8-n7-n6 To 0 Step -1
           Mpz_add(x5, x6, d2pow(5, n5))
           For n4 = n-n9-n8-n7-n6-n5 To 0 Step -1
             Mpz_add(x4, x5, d2pow(4, n4))
             For n3 = n-n9-n8-n7-n6-n5-n4 To 0 Step -1
               Mpz_add(x3, x4, d2pow(3, n3))
               For n2 = n-n9-n8-n7-n6-n5-n4-n3 To 0 Step -1
                 Mpz_add(x2, x3, d2pow(2, n2))
                 For n1 = n-n9-n8-n7-n6-n5-n4-n3-n2 To 0 Step -1
                   Mpz_add_ui(x1, x2, n1)
                   n0 = n-n9-n8-n7-n6-n5-n4-n3-n2-n1
                   Mpz_get_str(gmp_str, 10, x1)
                   If Len(*gmp_str) = n Then
                     ReDim d(10)
                     For i = 0 To n-1
                       d(gmp_str[i] - Asc("0")) += 1
                     Next i
                     If n9 = d(9) AndAlso n8 = d(8) AndAlso n7 = d(7) AndAlso n6 = d(6)_
                                  AndAlso n5 = d(5) AndAlso n4 = d(4) AndAlso n3 = d(3)_
                                  AndAlso n2 = d(2) AndAlso n1 = d(1) AndAlso n0 = d(0) Then
                       Print *gmp_str
                     End If
                   ElseIf Len(*gmp_str) < n Then
                     ' all for next loops have a negative step value
                     ' if len(str_x) becomes smaller then n it's time to try the next n value
                     ' GoTo label1   ' old school BASIC
                     ' prefered FreeBASIC style
                     Exit   For, For, For, For, For, For, For, For, For
                     ' leave n1,  n2,  n3,  n4,  n5,  n6,  n7,  n8,  n9 loop
                     ' and continue's after next n9
                   End If
                 Next n1
               Next n2
             Next n3
           Next n4
         Next n5
       Next n6
     Next n7
   Next n8
 Next n9
 ' label1:

Next n

' empty keyboard buffer While InKey <> "" : Wend Print : Print "hit any key to end program" Sleep End</lang>

Output:

Left side: program output, right side: sorted on length, value

9                                                                                            0
8                                                                                            1
7                                                                                            2
6                                                                                            3
5                                                                                            4
4                                                                                            5
3                                                                                            6
2                                                                                            7
1                                                                                            8
0                                                                                            9
407                                                                                        153
371                                                                                        370
370                                                                                        371
153                                                                                        407
9474                                                                                      1634
8208                                                                                      8208
1634                                                                                      9474
93084                                                                                    54748
92727                                                                                    92727
54748                                                                                    93084
548834                                                                                  548834
9926315                                                                                1741725
9800817                                                                                4210818
4210818                                                                                9800817
1741725                                                                                9926315
88593477                                                                              24678050
24678051                                                                              24678051
24678050                                                                              88593477
912985153                                                                            146511208
534494836                                                                            472335975
472335975                                                                            534494836
146511208                                                                            912985153
4679307774                                                                          4679307774
94204591914                                                                        32164049650
82693916578                                                                        32164049651
49388550606                                                                        40028394225
44708635679                                                                        42678290603
42678290603                                                                        44708635679
40028394225                                                                        49388550606
32164049651                                                                        82693916578
32164049650                                                                        94204591914
28116440335967                                                                  28116440335967
4338281769391371                                                              4338281769391370
4338281769391370                                                              4338281769391371
35875699062250035                                                            21897142587612075
35641594208964132                                                            35641594208964132
21897142587612075                                                            35875699062250035
4929273885928088826                                                        1517841543307505039
4498128791164624869                                                        3289582984443187032
3289582984443187032                                                        4498128791164624869
1517841543307505039                                                        4929273885928088826
63105425988599693916                                                      63105425988599693916
449177399146038697307                                                    128468643043731391252
128468643043731391252                                                    449177399146038697307
35452590104031691935943                                                21887696841122916288858
28361281321319229463398                                                27879694893054074471405
27907865009977052567814                                                27907865009977052567814
27879694893054074471405                                                28361281321319229463398
21887696841122916288858                                                35452590104031691935943
239313664430041569350093                                              174088005938065293023722
188451485447897896036875                                              188451485447897896036875
174088005938065293023722                                              239313664430041569350093
4422095118095899619457938                                            1550475334214501539088894
3706907995955475988644381                                            1553242162893771850669378
3706907995955475988644380                                            3706907995955475988644380
1553242162893771850669378                                            3706907995955475988644381
1550475334214501539088894                                            4422095118095899619457938
177265453171792792366489765                                        121204998563613372405438066
174650464499531377631639254                                        121270696006801314328439376
128851796696487777842012787                                        128851796696487777842012787
121270696006801314328439376                                        174650464499531377631639254
121204998563613372405438066                                        177265453171792792366489765
23866716435523975980390369295                                    14607640612971980372614873089
19008174136254279995012734741                                    19008174136254279995012734740
19008174136254279995012734740                                    19008174136254279995012734741
14607640612971980372614873089                                    23866716435523975980390369295
2309092682616190307509695338915                                1145037275765491025924292050346
1927890457142960697580636236639                                1927890457142960697580636236639
1145037275765491025924292050346                                2309092682616190307509695338915
17333509997782249308725103962772                              17333509997782249308725103962772
186709961001538790100634132976991                            186709961001538790100634132976990
186709961001538790100634132976990                            186709961001538790100634132976991
1122763285329372541592822900204593                          1122763285329372541592822900204593
12679937780272278566303885594196922                        12639369517103790328947807201478392
12639369517103790328947807201478392                        12679937780272278566303885594196922
1219167219625434121569735803609966019                    1219167219625434121569735803609966019
12815792078366059955099770545296129367                  12815792078366059955099770545296129367
115132219018763992565095597973971522401                115132219018763992565095597973971522400
115132219018763992565095597973971522400                115132219018763992565095597973971522401

FunL

<lang funl>def narcissistic( start ) =

 power = 1
 powers = array( 0..9 )
 def narc( n ) =
   num = n.toString()
   m = num.length()
   if power != m
     power = m
     powers( 0..9 ) = [i^m | i <- 0..9]
   if n == sum( powers(int(d)) | d <- num )
     n # narc( n + 1 )
   else
     narc( n + 1 )
 narc( start )

println( narcissistic(0).take(25) )</lang>

Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315]

Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. 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 storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

In this page you can see the program(s) related to this task and their results.

Go

Nothing fancy as it runs in a fraction of a second as-is. <lang go>package main

import "fmt"

func narc(n int) []int { power := [...]int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9} limit := 10 result := make([]int, 0, n) for x := 0; len(result) < n; x++ { if x >= limit { for i := range power { power[i] *= i // i^m } limit *= 10 } sum := 0 for xx := x; xx > 0; xx /= 10 { sum += power[xx%10] } if sum == x { result = append(result, x) } } return result }

func main() { fmt.Println(narc(25)) }</lang>

Output:
[0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315]

GW-BASIC

Translation of: FreeBASIC

Maximum for N (double) is14 digits, there are no 15 digits numbers <lang qbasic>1 DEFINT A-W : DEFDBL X-Z : DIM D(9) : DIM X2(9) : KEY OFF : CLS 2 FOR A = 0 TO 9 : X2(A) = A : NEXT A 3 FOR N = 1 TO 7 4 FOR N9 = N TO 0 STEP -1 5 FOR N8 = N-N9 TO 0 STEP -1 6 FOR N7 = N-N9-N8 TO 0 STEP -1 7 FOR N6 = N-N9-N8-N7 TO 0 STEP -1 8 FOR N5 = N-N9-N8-N7-N6 TO 0 STEP -1 9 FOR N4 = N-N9-N8-N7-N6-N5 TO 0 STEP -1 10 FOR N3 = N-N9-N8-N7-N6-N5-N4 TO 0 STEP -1 11 FOR N2 = N-N9-N8-N7-N6-N5-N4-N3 TO 0 STEP -1 12 FOR N1 = N-N9-N8-N7-N6-N5-N4-N3-N2 TO 0 STEP -1 13 N0 = N-N9-N8-N7-N6-N5-N4-N3-N2-N1 14 X = N1 + N2*X2(2) + N3*X2(3) + N4*X2(4) + N5*X2(5) + N6*X2(6) + N7*X2(7) + N8*X2(8) + N9*X2(9) 15 S$ = MID$(STR$(X),2) 16 IF LEN(S$) < N THEN GOTO 25 17 IF LEN(S$) <> N THEN GOTO 24 18 FOR A = 0 TO 9 : D(A) = 0 : NEXT A 19 FOR A = 0 TO N-1 20 B = ASC(MID$(S$,A+1,1))-48 21 D(B) = D(B) + 1 22 NEXT A 23 IF N0 = D(0) AND N1 = D(1) AND N2 = D(2) AND N3 = D(3) AND N4 = D(4) AND N5 = D(5) AND N6 = D(6) AND N7 = D(7) AND N8 = D(8) AND N9 = D(9) THEN PRINT X, 24 NEXT N1 : NEXT N2 : NEXT N3 : NEXT N4 : NEXT N5 : NEXT N6 : NEXT N7 : NEXT N8 : NEXT N9 25 FOR A = 2 TO 9 26 X2(A) = X2(A) * A 27 NEXT A 28 NEXT N 29 PRINT 30 PRINT "done" 31 END</lang>

Output:
 9             8             7             6             5
 4             3             2             1             0
 407           371           370           153           9474
 8208          1634          93084         92727         54748
 548834        9926315       9800817       4210818       1741725

Haskell

Exhaustive search (integer series)

<lang Haskell>import Data.Char (digitToInt)

isNarcissistic :: Int -> Bool isNarcissistic n = (sum ((^ digitCount) <$> digits) ==) n

 where
   digits = digitToInt <$> show n
   digitCount = length digits

main :: IO () main = mapM_ print $ take 25 (filter isNarcissistic [0 ..])</lang>

Reduced search (unordered digit combinations)

As summing the nth power of the digits is unaffected by digit order, we can reduce the search space by filtering digit combinations of given length and arbitrary order, rather than filtering a full integer sequence.

In this way we can find the 25th narcissistic number after length $ concatMap digitPowerSums [1 .. 7] == 19447 tests – an improvement on the exhaustive trawl through 9926315 integers.

<lang haskell>import Data.Bifunctor (second)

narcissiOfLength :: Int -> [Int] narcissiOfLength nDigits = snd <$> go nDigits []

 where
   powers = ((,) <*> (^ nDigits)) <$> [0 .. 9]
   go n parents
     | 0 < n = go (pred n) (f parents)
     | otherwise = filter (isDaffodil nDigits . snd) parents
     where
       f parents
         | null parents = powers
         | otherwise =
           parents >>=
           (\(d, pwrSum) -> second (pwrSum +) <$> take (succ d) powers)

isDaffodil :: Int -> Int -> Bool isDaffodil e n =

 (((&&) . (e ==) . length) <*> (n ==) . powerSum e) (digitList n)

powerSum :: Int -> [Int] -> Int powerSum n = foldr ((+) . (^ n)) 0

digitList :: Int -> [Int] digitList 0 = [0] digitList n = go n

 where
   go 0 = []
   go x = rem x 10 : go (quot x 10)

TEST ---------------------------

main :: IO () main =

 putStrLn $
 fTable
   "Narcissistic decimal numbers of length 1-7:\n"
   show
   show
   narcissiOfLength
   [1 .. 7]

fTable :: String -> (a -> String) -> (b -> String) -> (a -> b) -> [a] -> String fTable s xShow fxShow f xs =

 let rjust n c = drop . length <*> (replicate n c ++)
     w = maximum (length . xShow <$> xs)
 in unlines $
    s : fmap (((++) . rjust w ' ' . xShow) <*> ((" -> " ++) . fxShow . f)) xs</lang>
Output:
Narcissistic decimal numbers of length 1-7:

1 -> [0,1,2,3,4,5,6,7,8,9]
2 -> []
3 -> [153,370,371,407]
4 -> [1634,8208,9474]
5 -> [54748,92727,93084]
6 -> [548834]
7 -> [1741725,4210818,9800817,9926315]

Icon and Unicon

The following is a quick, dirty, and slow solution that works in both languages: <lang unicon>procedure main(A)

   limit := integer(A[1]) | 25
   every write(isNarcissitic(seq(0))\limit)

end

procedure isNarcissitic(n)

   sn := string(n)
   m := *sn
   every (sum := 0) +:= (!sn)^m
   return sum = n

end</lang>

Sample run:

->ndn
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315
->

J

<lang j>getDigits=: "."0@": NB. get digits from number isNarc=: (= +/@(] ^ #)@getDigits)"0 NB. test numbers for Narcissism</lang> Example Usage <lang j> (#~ isNarc) i.1e7 NB. display Narcissistic numbers 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315</lang>

Java

Works with: Java version 1.5+

<lang java5>public class Narc{ public static boolean isNarc(long x){ if(x < 0) return false;

String xStr = Long.toString(x); int m = xStr.length(); long sum = 0;

for(char c : xStr.toCharArray()){ sum += Math.pow(Character.digit(c, 10), m); } return sum == x; }

public static void main(String[] args){ for(long x = 0, count = 0; count < 25; x++){ if(isNarc(x)){ System.out.print(x + " "); count++; } } } }</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 
Works with: Java version 1.8

The statics and the System.exit(0) stem from having first developed a version that is not limited by the amount of narcisstic numbers that are to be calculated. I then read that this is a criterion and thus the implementation is an afterthought and looks awkwardish... but still... works! <lang java5> import java.util.stream.IntStream; public class NarcissisticNumbers {

   static int numbersToCalculate = 25;
   static int numbersCalculated = 0;
   
   public static void main(String[] args) {
       IntStream.iterate(0, n -> n + 1).limit(Integer.MAX_VALUE).boxed().forEach(i -> {
           int length = i.toString().length();
           int addedDigits = 0;
           
           for (int count = 0; count < length; count++) {
               int value = Integer.parseInt(String.valueOf(i.toString().charAt(count)));
               addedDigits += Math.pow(value, length);
           }
           if (i == addedDigits) {
               numbersCalculated++;
               System.out.print(addedDigits + " ");
           }
           if (numbersCalculated == numbersToCalculate) {
               System.exit(0);
           }
       });
   }

}</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 

JavaScript

ES5

Translation of: Java

<lang javascript>function isNarc(x) {

   var str = x.toString(),
       i,
       sum = 0,
       l = str.length;
   if (x < 0) {
       return false;
   } else {
       for (i = 0; i < l; i++) {
           sum += Math.pow(str.charAt(i), l);
       }
   }
   return sum == x;

} function main(){

   var n = []; 
   for (var x = 0, count = 0; count < 25; x++){
       if (isNarc(x)){
           n.push(x);
           count++;
       }
   }
   return n.join(' '); 

}</lang>

Output:
"0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315"

ES6

Exhaustive search (integer series)

<lang JavaScript>(() => {

   'use strict';

   // digits :: Int -> [Int]
   const digits = n => n.toString()
       .split()
       .map(x => parseInt(x, 10));

   // pow :: Int -> Int -> Int
   const pow = Math.pow;

   // isNarc :: Int -> Bool
   const isNarc = n => {
       const
           ds = digits(n),
           len = ds.length;

       return ds.reduce((a, x) =>
           a + pow(x, len), 0) === n;
   };

   // until :: (a -> Bool) -> (a -> a) -> a -> a
   const until = (p, f, x) => {
       let v = x;
       while (!p(v)) v = f(v);
       return v;
   };

   return until(
           x => x.narc.length > 24,
           x => ({
               n: x.n + 1,
               narc: (isNarc(x.n) ? x.narc.concat(x.n) : x.narc)
           }), {
               n: 0,
               narc: []
           }
       )
       .narc

})();</lang>

Output:

<lang JavaScript>[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315]</lang>


Reduced search (unordered digit combinations)

Translation of: Haskell

As summing the nth power of the digits is unaffected by digit order, we can reduce the search space by filtering digit combinations of given length and arbitrary order, rather than filtering a full integer sequence.

In this way we can find the 25th narcissistic number after length(concatMap(digitPowerSums, enumFromTo(0, 7))) === 19447 tests – an improvement on the exhaustive trawl through 9926315 integers.

(Generating the unordered digit combinations directly as power sums allows faster testing later, and needs less space) <lang JavaScript>(() => {

   'use strict';
   // main :: IO ()
   const main = () =>
       console.log(
           fTable(
               'Narcissistic decimal numbers of lengths [1..7]:\n'
           )(show)(show)(
               narcissiOfLength
           )(enumFromTo(1)(7))
       );
   // narcissiOfLength :: Int -> [Int]
   const narcissiOfLength = n =>
       0 < n ? filter(isDaffodil(n))(
           digitPowerSums(n)
       ) : [0];


   // powerSum :: Int -> [Int] -> Int
   const powerSum = n =>
       xs => xs.reduce(
           (a, x) => a + pow(x, n), 0
       );


   // isDaffodil :: Int -> Int -> Bool
   const isDaffodil = e => n => {
       // True if the decimal digits of N,
       // each raised to the power E, sum to N.
       const ds = digitList(n);
       return e === ds.length && n === powerSum(e)(ds);
   };
   // The subset of integers of n digits that actually need daffodil checking:
   // (Flattened leaves of a tree of unique digit combinations, in which
   // order is not significant. Digit sequence doesn't affect power summing)
   // digitPowerSums :: Int -> [Int]
   const digitPowerSums = nDigits => {
       const
           digitPowers = map(x => [x, pow(x, nDigits)])(
               enumFromTo(0)(9)
           ),
           treeGrowth = (n, parentPairs) => 0 < n ? (
               treeGrowth(n - 1,
                   isNull(parentPairs) ? (
                       digitPowers
                   ) : concatMap(
                       ([parentDigit, parentSum]) =>
                       map(([leafDigit, leafSum]) => //
                           [leafDigit, parentSum + leafSum])(
                           take(parentDigit + 1)(digitPowers)
                       )
                   )(parentPairs)
               )
           ) : parentPairs;
       return map(snd)(treeGrowth(nDigits, []));
   };


   // ---------------------GENERIC FUNCTIONS---------------------
   // enumFromTo :: Int -> Int -> [Int]
   const enumFromTo = m => n =>
       Array.from({
           length: 1 + n - m
       }, (_, i) => m + i);
   // concatMap :: (a -> [b]) -> [a] -> [b]
   const concatMap = f =>
       xs => xs.flatMap(f);
   // cons :: a -> [a] -> [a]
   const cons = x =>
       xs => [x].concat(xs);
   // digitList :: Int -> [Int]
   const digitList = n => {
       const go = x => 0 < x ? (
           cons(x % 10)(
               go(Math.floor(x / 10))
           )
       ) : [];
       return 0 < n ? go(n) : [0];
   }
   // filter :: (a -> Bool) -> [a] -> [a]
   const filter = f => xs => xs.filter(f);
   // map :: (a -> b) -> [a] -> [b]
   const map = f =>
       xs => xs.map(f);
   // isNull :: [a] -> Bool
   // isNull :: String -> Bool
   const isNull = xs =>
       1 > xs.length;
   // length :: [a] -> Int
   const length = xs => xs.length;
   // pow :: Int -> Int -> Int
   const pow = Math.pow;
   // take :: Int -> [a] -> [a]
   const take = n =>
       xs => xs.slice(0, n);
   // snd :: (a, b) -> b
   const snd = tpl => tpl[1];
   // show :: a -> String
   const show = x => JSON.stringify(x)
   // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
   const zipWith = f => xs => ys =>
       xs.slice(
           0, Math.min(xs.length, ys.length)
       ).map((x, i) => f(x)(ys[i]));
   // ------------------------FORMATTING-------------------------
   // fTable :: String -> (a -> String) -> (b -> String)
   //                      -> (a -> b) -> [a] -> String
   const fTable = s => xShow => fxShow => f => xs => {
       // Heading -> x display function ->
       //           fx display function ->
       //    f -> values -> tabular string
       const
           ys = xs.map(xShow),
           w = Math.max(...ys.map(length));
       return s + '\n' + zipWith(
           a => b => a.padStart(w, ' ') + ' -> ' + b
       )(ys)(
           xs.map(x => fxShow(f(x)))
       ).join('\n');
   };
   // MAIN ---
   return main();

})();</lang>

Output:
Narcissistic decimal numbers of lengths [1..7]:

1 -> [0,1,2,3,4,5,6,7,8,9]
2 -> []
3 -> [153,370,371,407]
4 -> [1634,8208,9474]
5 -> [54748,92727,93084]
6 -> [548834]
7 -> [1741725,4210818,9800817,9926315]

jq

Works with: jq version 1.4

A function for checking whether a given non-negative integer is narcissistic could be implemented in jq as follows: <lang jq>def is_narcissistic:

 def digits: tostring | explode[] | [.] | implode | tonumber;
 def pow(n): . as $x | reduce range(0;n) as $i (1; . * $x);
 (tostring | length) as $len
 | . == reduce digits as $d (0;  . + ($d | pow($len)) )
 end;</lang>

In the following, this definition is modified to avoid recomputing (d ^ i). This is accomplished introducing the array [i, [0^i, 1^i, ..., 9^i]]. To update this array for increasing values of i, the function powers(j) is defined as follows: <lang jq># Input: [i, [0^i, 1^i, 2^i, ..., 9^i]]

  1. Output: [j, [0^j, 1^j, 2^j, ..., 9^j]]
  2. provided j is i or (i+1)

def powers(j):

 if .[0] == j then .
 else .[0] += 1
 | reduce range(0;10) as $k (.; .[1][$k] *= $k)
 end;</lang>

The function is_narcisstic can now be modified to use powers(j) as follows: <lang jq># Input: [n, [i, [0^i, 1^i, 2^i,...]]] where i is the number of digits in n. def is_narcissistic:

 def digits: tostring | explode[] | [.] | implode | tonumber;
 .[1][1] as $powers
 | .[0]
 | if . < 0 then false
   else . == reduce digits as $d (0;  . + $powers[$d] )
   end;</lang>

The task <lang jq># If your jq has "while", then feel free to omit the following definition: def while(cond; update):

 def _while:  if cond then ., (update | _while) else empty end; 
 _while;
  1. The first k narcissistic numbers, beginning with 0:

def narcissistic(k):

 # State: [n, is_narcissistic, count, [len, [0^len, 1^len, ...]]]
 # where len is the number of digits in n.
 [0, true, 1, [1, [range(0;10)]]]
 | while( .[2] <= k;
          .[3] as $powers
          | (.[0]+1) as $n
          | ($n | tostring | length) as $len

| ($powers | powers($len)) as $powersprime | if [$n, $powersprime] | is_narcissistic then [$n, true, .[2] + 1, $powersprime] else [$n, false, .[2], $powersprime ] end )

 | select(.[1])
 | "\(.[2]): \(.[0])" ;

narcissistic(25)</lang>

Output:

<lang sh>jq -r -n -f Narcissitic_decimal_number.jq 1: 0 2: 1 3: 2 4: 3 5: 4 6: 5 7: 6 8: 7 9: 8 10: 9 11: 153 12: 370 13: 371 14: 407 15: 1634 16: 8208 17: 9474 18: 54748 19: 92727 20: 93084 21: 548834 22: 1741725 23: 4210818 24: 9800817 25: 9926315</lang>

Julia

This easy to implement brute force technique is plenty fast enough to find the first few Narcissistic decimal numbers. <lang Julia>using Printf # for Julia version 1.0+

function isnarcissist(n, b=10)

   -1 < n || return false
   d = digits(n, base=b)
   m = length(d)
   n == mapreduce((x)->x^m, +, d)

end

function findnarcissist(verbose=false)

   goal = 25
   ncnt = 0
   verbose && println("Finding the first ", goal, " Narcissistic numbers:")
   for i in 0:typemax(1)
       isnarcissist(i) || continue
       ncnt += 1
       verbose && println(@sprintf "    %2d %7d" ncnt i)
       ncnt < goal || break
   end

end

findnarcissist() @time findnarcissist(true)

</lang>
Output:
Finding the first 25 Narcissistic numbers:
     1       0
     2       1
     3       2
     4       3
     5       4
     6       5
     7       6
     8       7
     9       8
    10       9
    11     153
    12     370
    13     371
    14     407
    15    1634
    16    8208
    17    9474
    18   54748
    19   92727
    20   93084
    21  548834
    22 1741725
    23 4210818
    24 9800817
    25 9926315
  3.054463 seconds (19.90 M allocations: 1.466 GiB, 14.27% gc time)

Kotlin

<lang scala>// version 1.1.0

fun isNarcissistic(n: Int): Boolean {

   if (n < 0) throw IllegalArgumentException("Argument must be non-negative")
   var nn = n
   val digits = mutableListOf<Int>()
   val powers = IntArray(10) { 1 } 
   while (nn > 0) {
      digits.add(nn % 10)
      for (i in 1..9) powers[i] *= i // no need to calculate powers[0]
      nn /= 10
   }
   val sum = digits.filter { it > 0 }.map { powers[it] }.sum()
   return n == sum

}

fun main(args: Array<String>) {

   println("The first 25 narcissistic (or Armstrong) numbers are:")
   var i = 0
   var count = 0
   do {
       if (isNarcissistic(i)) {
           print("$i ")
           count++
       }
       i++
   }
   while (count < 25)    

}</lang>

Output:
The first 25 narcissistic (or Armstrong) numbers are:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Ksh

<lang ksh>

  1. !/bin/ksh
  1. Narcissistic decimal number
  1. # Variables:
  1. # Functions:
  1. # Function _isnarcissist(n) - return 1 if n is a narcissistic decimal number

function _isnarcissist { typeset _n ; integer _n=$1

(( ${_n} == $(_sumpowdigits ${_n}) )) && return 1 return 0 }

  1. # Function _sumpowdigits(n) - return sum of the digits raised to #digit power

function _sumpowdigits { typeset _n ; integer _n=$1 typeset _i ; typeset -si _i typeset _sum ; integer _sum=0

for ((_i=0; _i<${#_n}; _i++)); do (( _sum+=(${_n:_i:1}**${#_n}) )) done echo ${_sum} }

######
  1. main #
######

integer i cnt=0 for ((i=0; cnt<25; i++)); do _isnarcissist ${i} ; (( $? )) && printf "%3d. %d\n" $(( ++cnt )) ${i} done </lang>

Output:

 1. 0
 2. 1
 3. 2
 4. 3
 5. 4
 6. 5
 7. 6
 8. 7
 9. 8
10. 9
11. 153
12. 370
13. 371
14. 407
15. 1634
16. 8208
17. 9474
18. 54748
19. 92727
20. 93084
21. 548834
22. 1741725
23. 4210818
24. 9800817
25. 9926315

Lua

This is a simple/naive/slow method but it still spits out the requisite 25 in less than a minute using LuaJIT on a 2.5 GHz machine. <lang Lua>function isNarc (n)

   local m, sum, digit = string.len(n), 0
   for pos = 1, m do
       digit = tonumber(string.sub(n, pos, pos))
       sum = sum + digit^m
   end
   return sum == n

end

local n, count = 0, 0 repeat

   if isNarc(n) then
       io.write(n .. " ")
       count = count + 1
   end
   n = n + 1

until count == 25</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Maple

<lang Maple>

Narc:=proc(i) local num,len,j,sums: sums:=0: num := parse~(StringTools:-Explode((convert(i,string)))): len:=numelems(num): for j from 1 to len do sums:=sums+(num[j]^(len)): end do; if sums = i then return i; else return NULL; end if; end proc:

i:=0: NDN:=[]: while numelems(NDN)<25 do NDN:=[op(NDN),(Narc(i))]: i:=i+1: end do: NDN; </lang>

Mathematica/Wolfram Language

<lang Mathematica>narc[1] = 0; narc[n_] := narc[n] = NestWhile[# + 1 &, narc[n - 1] + 1, Plus @@ (IntegerDigits[#]^IntegerLength[#]) != # &]; narc /@ Range[25]</lang>

Output:
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315}

MATLAB

<lang MATLAB>function testNarcissism

   x = 0;
   c = 0;
   while c < 25
       if isNarcissistic(x)
           fprintf('%d ', x)
           c = c+1;
       end
       x = x+1;
   end
   fprintf('\n')

end

function tf = isNarcissistic(n)

   dig = sprintf('%d', n) - '0';
   tf = n == sum(dig.^length(dig));

end</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Nanoquery

<lang Nanoquery>def is_narcissist(num) digits = {} for digit in str(num) digits.append(int(digit)) end

sum = 0 for digit in digits sum += digit ^ len(num) end

return sum = num end

def narcissist(n) results = {}

i = 0 while len(results) < n if is_narcissist(i) results.append(i) end i += 1 end

return results end

// get 25 narcissist numbers for num in narcissist(25) print num + " " end println</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 

Nim

A simple solution which runs in about one second. <lang Nim>import sequtils, strutils

func digits(n: Natural): seq[int] =

 result.add n mod 10
 var n = n div 10
 while n != 0:
   result.add n mod 10
   n = n div 10

proc findNarcissistic(count: Natural): seq[int] =

 var
   n = 0
   m = 10
   powers = toseq(0..9)
 while true:
   while n < m:
     var s = 0
     for d in n.digits:
       inc s, powers[d]
     if s == n:
       result.add n
       if result.len == count: return
     inc n
   for i in 0..9: powers[i] *= i
   m *= 10

echo findNarcissistic(25).join(" ")</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Oforth

<lang Oforth>: isNarcissistic(n) | i m |

  n 0 while( n ) [ n 10 /mod ->n swap 1 + ] ->m
  0 m loop: i [ swap m pow + ] == ;

genNarcissistic(n)

| l |

  ListBuffer new dup ->l
  0 while(l size n <>) [ dup isNarcissistic ifTrue: [ dup l add ] 1 + ] drop ;

</lang>

Output:
>genNarcissistic(25) .
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084,
548834, 1741725, 4210818, 9800817, 9926315] ok

PARI/GP

Naive code, could be improved by splitting the digits in half and meeting in the middle. <lang parigp>isNarcissistic(n)=my(v=digits(n)); sum(i=1, #v, v[i]^#v)==n v=List();for(n=1,1e9,if(isNarcissistic(n),listput(v,n);if(#v>24, return(Vec(v)))))</lang>

Output:
%1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315, 24678050]

Pascal

Free Pascal

A recursive version starting at the highest digit and recurses to digit 0. Bad runtime. One more digit-> 10x runtime runtime ~ 10^(count of Digits). <lang pascal> program NdN; //Narcissistic decimal number const

 Base = 10;
 MaxDigits = 16;

type

 tDigit = 0..Base-1;
 tcntDgt= 0..MaxDigits-1;

var

 powDgt   : array[tDigit]  of NativeUint;
 PotdgtPos: array[tcntDgt] of NativeUint;
 UpperSum : array[tcntDgt] of NativeUint;
 tmpSum,
 tmpN,
 actPot  : NativeUint;

procedure InitPowDig; var

 i,j : NativeUint;

Begin

 j := 1;
 For i := 0 to High(tDigit) do
 Begin
   powDgt[i] := i;
   PotdgtPos[i] := j;
   j := j*Base;
 end;
 actPot := 0;

end;

procedure NextPowDig; var

 i,j : NativeUint;

Begin

 // Next power of digit =  i ^ actPot,always 0 = 0 , 1 = 1
 For i := 2 to High(tDigit) do
   powDgt[i] := powDgt[i]*i;
 // number of digits times 9 ^(max number of digits)
 j := powDgt[High(tDigit)];
 For i := 0 to High(UpperSum) do
   UpperSum[i] := (i+1)*j;
 inc(actPot);

end; procedure OutPutNdN(n:NativeUint); Begin

 write(n,' ');

end;

procedure NextDgtSum(dgtPos,i,sumPowDgt,n:NativeUint); begin

 //unable to reach sum
 IF (sumPowDgt+UpperSum[dgtPos]) < n then
   EXIT;
 repeat
   tmpN   := n+PotdgtPos[dgtPos]*i;
   tmpSum := sumPowDgt+powDgt[i];
   //unable to get smaller
   if tmpSum > tmpN then
     EXIT;
   IF tmpSum = tmpN then
     OutPutNdN(tmpSum);
   IF dgtPos>0 then
     NextDgtSum(dgtPos-1,0,tmpSum,tmpN);
   inc(i);
 until i >= Base;

end;

var

 i : NativeUint;

Begin

 InitPowDig;
 For i := 1 to 9 do
 Begin
   write(' length ',actPot+1:2,': ');
   //start with 1 in front, else you got i-times 0 in front
   NextDgtSum(actPot,1,0,0);
   writeln;
   NextPowDig;
 end;

end.</lang>

output
 time ./NdN
 length  1: 1 2 3 4 5 6 7 8 9 
 length  2: 
 length  3: 153 370 370 371 407 
 length  4: 1634 8208 9474 
 length  5: 54748 92727 93084 
 length  6: 548834 
 length  7: 1741725 4210818 9800817 9926315 
 length  8: 24678050 24678050 24678051 88593477 
 length  9: 146511208 472335975 534494836 912985153 

real	0m1.000s

alternative

recursive solution.Just counting the different combination of digits
See Combinations_with_repetitions
<lang pascal>program PowerOwnDigits; {$IFDEF FPC}

 {$MODE DELPHI}{$OPTIMIZATION ON,ALL}{$COPERATORS ON}

{$ELSE}{$APPTYPE CONSOLE}{$ENDIF} uses

 SysUtils;

const

 MAXBASE = 10;
 MaxDgtVal = MAXBASE - 1;
 MaxDgtCount = 19;

type

 tDgtCnt = 0..MaxDgtCount;
 tValues = 0..MaxDgtVal;
 tUsedDigits = array[0..23] of Int8;
 tpUsedDigits = ^tUsedDigits;
 tPower = array[tValues] of Uint64;

var

 PowerDgt: array[tDgtCnt] of tPower;
 Min10Pot : array[tDgtCnt] of Uint64;
 gblUD  : tUsedDigits;
 CombIdx: array of Int8;
 Numbers : array of Uint64;
 rec_cnt : NativeInt;
 procedure OutUD(const UD:tUsedDigits);
 var
   i : integer;
 begin
   For i in tValues do
     write(UD[i]:3);
   writeln;
   For i := 0 to MaxDgtCount do
     write(CombIdx[i]:3);
   writeln;
 end;
 function InitCombIdx(ElemCount: Byte): pbyte;
 begin
   setlength(CombIdx, ElemCount + 1);
   Fillchar(CombIdx[0], sizeOf(CombIdx[0]) * (ElemCount + 1), #0);
   Result := @CombIdx[0];
   Fillchar(gblUD[0], sizeOf(gblUD[0]) * (ElemCount + 1), #0);
   gblUD[0]:= 1;
 end;
 function Init(ElemCount:byte):pByte;
 var
   pP1,Pp2 : pUint64;
   i, j: Int32;
 begin
   Min10Pot[0]:= 0;
   Min10Pot[1]:= 1;
   for i := 2 to High(tDgtCnt) do
     Min10Pot[i]:=Min10Pot[i-1]*MAXBASE;
   pP1 := @PowerDgt[low(tDgtCnt)];
   for i in tValues do
     pP1[i] := 1;
   pP1[0] := 0;
   for j := low(tDgtCnt) + 1 to High(tDgtCnt) do
   Begin
     pP2 := @PowerDgt[j];
     for i in tValues do
       pP2[i] := pP1[i]*i;
     pP1 := pP2;
   end;
   result := InitCombIdx(ElemCount);
   gblUD[0]:= 1;
 end;
 function GetPowerSum(minpot:nativeInt;digits:pbyte;var UD :tUsedDigits):NativeInt;
 var
   pPower : pUint64;
   res,r  : Uint64;
   dgt :Int32;
 begin
   r := Min10Pot[minpot];
   dgt := minpot;
   res := 0;
   pPower := @PowerDgt[minpot,0];
   repeat
     dgt -=1;
     res += pPower[digits[dgt]];
   until dgt=0;
   //check if res within bounds of digitCnt
   result := 0;
   if (res<r) or (res>r*MAXBASE) then  EXIT;
   //convert res into digits
   repeat
     r := res DIV MAXBASE;
     result+=1;
     UD[res-r*MAXBASE]-= 1;
     res := r;
   until r = 0;
 end;
 procedure calcNum(minPot:Int32;digits:pbyte);
 var
   UD :tUsedDigits;
   res: Uint64;
   i: nativeInt;
 begin
   UD := gblUD;
   If GetPowerSum(minpot,digits,UD) <>0 then
   Begin
     //don't check 0
     i := 1;
     repeat
       If UD[i] <> 0 then
         Break;
       i +=1;
     until i > MaxDgtVal;
     if i > MaxDgtVal then
     begin
       res := 0;
       for i := minpot-1 downto 0 do
         res += PowerDgt[minpot,digits[i]];
       setlength(Numbers, Length(Numbers) + 1);
       Numbers[high(Numbers)] := res;
     end;
   end;
 end;
 function NextCombWithRep(pComb: pByte;pUD :tpUsedDigits;MaxVal, ElemCount: UInt32): boolean;
 var
   i,dgt: NativeInt;
 begin
   i := -1;
   repeat
     i += 1;
     dgt := pComb[i];
     if dgt < MaxVal then
       break;
     dec(pUD^[dgt]);
   until i >= ElemCount;
   Result := i >= ElemCount;
   if i = 0 then
   begin
     dec(pUD^[dgt]);
     dgt +=1;
     pComb[i] := dgt;
     inc(pUD^[dgt]);
   end
   else
   begin
     //decrements digit 0 too.This is false, but not checked. 
     dec(pUD^[dgt]);
     dgt +=1;
     pUD^[dgt]:=i+1;
     repeat
       pComb[i] := dgt;
       i -= 1;
     until i < 0;
   end;
 end;

var

 digits : pByte;
 T0 : Int64;
 tmp: Uint64;
 i, j : Int32;

begin

 digits := Init(MaxDgtCount);
 T0 := GetTickCount64;
 rec_cnt := 0;
 // i > 0
 For i := 2 to MaxDgtCount do
 Begin
   digits := InitCombIdx(MaxDgtCount);
   repeat
     calcnum(i,digits);
     inc(rec_cnt);
   until NextCombWithRep(digits,@gblUD,MaxDgtVal,i);
   writeln(i:3,' digits with ',Length(Numbers):3,' solutions in ',GetTickCount64-T0:5,' ms');
 end;
 T0 := GetTickCount64-T0;
 writeln(rec_cnt,' recursions');
 //sort
 for i := 0 to High(Numbers) - 1 do
   for j := i + 1 to High(Numbers) do
     if Numbers[j] < Numbers[i] then
     begin
       tmp := Numbers[i];
       Numbers[i] := Numbers[j];
       Numbers[j] := tmp;
     end;
 setlength(Numbers, j + 1);
 for i := 0 to High(Numbers) do
    writeln(i+1:3,Numbers[i]:20);
 setlength(Numbers, 0);
 setlength(CombIdx,0);
 {$IFDEF WINDOWS}
 readln;
 {$ENDIF}

end. </lang>

@TIO.RUN:
  2 digits with   0 solutions in     0 ms
  3 digits with   4 solutions in     0 ms
  4 digits with   7 solutions in     0 ms
  5 digits with  10 solutions in     0 ms
  6 digits with  11 solutions in     0 ms
  7 digits with  15 solutions in     0 ms
  8 digits with  18 solutions in     1 ms
  9 digits with  22 solutions in     3 ms
 10 digits with  23 solutions in     6 ms
 11 digits with  31 solutions in    13 ms
 12 digits with  31 solutions in    25 ms
 13 digits with  31 solutions in    46 ms
 14 digits with  32 solutions in    82 ms
 15 digits with  32 solutions in   141 ms
 16 digits with  34 solutions in   238 ms
 17 digits with  37 solutions in   395 ms
 18 digits with  37 solutions in   644 ms
 19 digits with  41 solutions in  1028 ms
20029999 recursions
  1                 153
  2                 370
  3                 371
  4                 407
  5                1634
  6                8208
  7                9474
  8               54748
  9               92727
 10               93084
 11              548834
 12             1741725
 13             4210818
 14             9800817
 15             9926315
 16            24678050
 17            24678051
 18            88593477
 19           146511208
 20           472335975
 21           534494836
 22           912985153
 23          4679307774
 24         32164049650
 25         32164049651
 26         40028394225
 27         42678290603
 28         44708635679
 29         49388550606
 30         82693916578
 31         94204591914
 32      28116440335967
 33    4338281769391370
 34    4338281769391371
 35   21897142587612075
 36   35641594208964132
 37   35875699062250035
 38 1517841543307505039
 39 3289582984443187032
 40 4498128791164624869
 41 4929273885928088826

Perl

Simple version using a naive predicate. About 15 seconds. <lang perl>sub is_narcissistic {

 my $n = shift;
 my($k,$sum) = (length($n),0);
 $sum += $_**$k for split(//,$n);
 $n == $sum;

} my $i = 0; for (1..25) {

 $i++ while !is_narcissistic($i);
 say $i++;

}</lang>

Phix

with javascript_semantics
function narcissistic(integer n)
    string d = sprintf("%d",n)
    integer l = length(d)
    atom sumn = 0
    for i=1 to l do
        sumn += power(d[i]-'0',l)
    end for
    return sumn=n
end function

sequence s = {}
integer n = 0
while length(s)<25 do
    if narcissistic(n) then s &= n end if
    n += 1
end while
pp(s)
Output:
{0,1,2,3,4,5,6,7,8,9,153,370,371,407,1634,8208,9474,54748,92727,93084,548834,1741725,4210818,9800817,9926315}

faster

Translation of: AppleScript

At least 100 times faster, gets the first 47 (the native precision limit) before the above gets the first 25.
I tried a gmp version, but it was 20-odd times slower, presumably because it uses that mighty sledgehammer for many small int cases.

with javascript_semantics
-- Begin with zero, which is narcissistic by definition and is never the only digit used in other numbers.
sequence output = {`0`}
bool done = false
integer m = 0
integer q
atom t0 = time()
 
procedure recurse(string digits, atom powsum, integer rem)
    -- Recursive subhandler. Builds lists containing m digit values while summing the digits' mth powers.
    -- If m digits have been obtained, compare the sum of powers's digits with the values in the list.
    -- Otherwise continue branching the recursion to derive longer lists.
    if rem=0 then
        atom temp = powsum
        integer unmatched = m
        while temp do
            integer d = find('0'+remainder(temp,10),digits)
            if d=0 then exit end if
            digits[d] = ' '
            unmatched -= 1
            temp = floor(temp/10)
        end while
        -- If all the digits have been matched, the sum of powers is narcissistic.
        if unmatched=0 then
            output = append(output,sprintf("%d",powsum))
            if length(output)=q then done = true end if
        end if
    else
        -- If fewer than m digits at this level, derive longer lists from the current one.
        -- Adding only values that are less than or equal to the last one makes each
        -- collection unique and turns up the narcissistic numbers in numerical order.
        --
        -- ie/eg if sum(sq_power({9,7,4,4},4))==9474, and as shown sort(digits)==list,
        -- then 9474 is the one and only permutation that is narcissistic, obviously,
        -- and there is no point looking at any other permutation of that list, ever.
        -- Also 1000,1100,1110,1111 are the only 4 lists beginning 1, as opposed to 
        -- the 999 four-digit numbers beginning 1 that might otherwise be checked,
        -- and likewise 9000..9999 is actually just 220 rather than the full 999.
        -- (I can see that exploring smaller partial sums first will tend to issue
        --  results in numeric order, but cannot see an absolute certainty of that)
        --
        for d=0 to digits[$]-'0' do
            recurse(digits & d+'0', powsum + power(d,m), rem-1)
            if done then exit end if
        end for
    end if
end procedure
 
function narcissisticDecimalNumbers(integer qp)
    atom t1 = time()+1
    q = qp
    -- Initiate the recursive building and testing of collections of increasing numbers of digit values.
    while not done do
        m += 1
        if m > iff(machine_bits()=32?16:17) then
            output = append(output,"Remaining numbers beyond number precision")
            done = true
        else
            for digit=1 to 9 do
                recurse(""&'0'+digit, power(digit,m), m-1)
                if done then exit end if
            end for
            if not done and time()>t1 and platform()!=JS then
                printf(1,"searching... %d found, length %d, %s\n",
                         {length(output),m,elapsed(time()-t0)})
                t1 = time()+1
            end if
        end if
    end while
    return output
end function
 
sequence r = narcissisticDecimalNumbers(iff(machine_bits()=32?44:47))
pp(r)
printf(1,"found %d in %s\n",{length(r),elapsed(time()-t0)})
Output:
searching... 41 found, length 13, 1.0s
searching... 42 found, length 15, 3.3s
searching... 44 found, length 16, 5.7s
{`0`, `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, `9`, `153`, `370`, `371`,
 `407`, `1634`, `8208`, `9474`, `54748`, `92727`, `93084`, `548834`,
 `1741725`, `4210818`, `9800817`, `9926315`, `24678050`, `24678051`,
 `88593477`, `146511208`, `472335975`, `534494836`, `912985153`,
 `4679307774`, `32164049650`, `32164049651`, `40028394225`, `42678290603`,
 `44708635679`, `49388550606`, `82693916578`, `94204591914`,
 `28116440335967`, `4338281769391370`, `4338281769391371`,
 `21897142587612075`, `35641594208964132`, `35875699062250035`}
found 47 in 8.2s

PicoLisp

<lang PicoLisp>(let (C 25 N 0 L 1)

  (loop
     (when 
        (=
           N
           (sum ** (mapcar format (chop N)) (need L L)) )
        (println N)
        (dec 'C) )
     (inc 'N)   
     (setq L (length N))
     (T (=0 C) 'done) ) )
     

(bye)</lang>

PL/I

version 1

Translation of: REXX

<lang pli> narn: Proc Options(main);

Dcl (j,k,l,nn,n,sum) Dec Fixed(15)init(0);
Dcl s Char(15) Var;
Dcl p(15) Pic'9' Based(addr(s));
Dcl (ms,msa,ela) Dec Fixed(15);
Dcl tim Char(12);
n=30;
ms=milliseconds();
Do j=0 By 1 Until(nn=n);
  s=dec2str(j);
  l=length(s);
  sum=left(s,1)**l;
  Do k=2 To l;
    sum=sum+substr(s,k,1)**l;
    If sum>j Then Leave;
    End;
  If sum=j Then Do
    nn=nn+1;
    msa=milliseconds();
    ela=msa-ms;
    /*Put Skip Data(ms,msa,ela);*/
    ms=msa;                            /*yyyymmddhhmissmis*/
    tim=translate('ij:kl:mn.opq',datetime(),'abcdefghijklmnopq');
    Put Edit(nn,' narcissistic:',j,ela,tim)
            (Skip,f(9),a,f(12),f(15),x(2),a(12));
    End;
  End;
dec2str: Proc(x) Returns(char(16) var);
Dcl x Dec Fixed(15);
Dcl ds Pic'(14)z9';
ds=x;
Return(trim(ds));
End;
milliseconds: Proc Returns(Dec Fixed(15));
Dcl c17 Char(17);
dcl 1 * Def C17,
     2 * char(8),
     2 hh Pic'99',
     2 mm Pic'99',
     2 ss Pic'99',
     2 ms Pic'999';
Dcl result Dec Fixed(15);
c17=datetime();
result=(((hh*60+mm)*60)+ss)*1000+ms;
/*
Put Edit(translate('ij:kl:mn.opq',datetime(),'abcdefghijklmnopq'),
         result)
        (Skip,a(12),F(15));
*/
Return(result);
End
End;</lang>
Output:
       1 narcissistic:           0              0  16:10:17.586
        2 narcissistic:           1              0  16:10:17.586
        3 narcissistic:           2              0  16:10:17.586
        4 narcissistic:           3              0  16:10:17.586
        5 narcissistic:           4              0  16:10:17.586
        6 narcissistic:           5              0  16:10:17.586
        7 narcissistic:           6              0  16:10:17.586
        8 narcissistic:           7              0  16:10:17.586
        9 narcissistic:           8              0  16:10:17.586
       10 narcissistic:           9              0  16:10:17.586
       11 narcissistic:         153              0  16:10:17.586
       12 narcissistic:         370              0  16:10:17.586
       13 narcissistic:         371              0  16:10:17.586
       14 narcissistic:         407              0  16:10:17.586
       15 narcissistic:        1634             10  16:10:17.596
       16 narcissistic:        8208             30  16:10:17.626
       17 narcissistic:        9474             10  16:10:17.636
       18 narcissistic:       54748            210  16:10:17.846
       19 narcissistic:       92727            170  16:10:18.016
       20 narcissistic:       93084              0  16:10:18.016
       21 narcissistic:      548834           1630  16:10:19.646
       22 narcissistic:     1741725           4633  16:10:24.279
       23 narcissistic:     4210818          10515  16:10:34.794
       24 narcissistic:     9800817          28578  16:11:03.372
       25 narcissistic:     9926315            510  16:11:03.882
       26 narcissistic:    24678050          73077  16:12:16.959
       27 narcissistic:    24678051              0  16:12:16.959
       28 narcissistic:    88593477         365838  16:18:22.797
       29 narcissistic:   146511208         276228  16:22:59.025
       30 narcissistic:   472335975        1682125  16:51:01.150 

version 2

Precompiled powers <lang>*process source xref attributes or(!);

narn3: Proc Options(main);
Dcl (i,j,k,l,nn,n,sum) Dec Fixed(15)init(0);
Dcl s  Char(15) Var;
dcl t  Char(15);
Dcl p9(15) Pic'9' Based(addr(t));
Dcl (ms,msa,ela) Dec Fixed(15);
Dcl tim Char(12);
n=30;
Dcl power(0:9,1:9) Dec Fixed(15);
Do i=0 To 9;
  Do j=1 To 9;
    Power(i,j)=i**j;
    End;
  End;
ms=milliseconds();
Do j=0 By 1 Until(nn=n);
  s=dec2str(j);
  t=s;
  l=length(s);
  sum=power(p9(1),l);
  Do k=2 To l;
    sum=sum+power(p9(k),l);
    If sum>j Then Leave;
    End;
  If sum=j Then Do;
    nn=nn+1;
    msa=milliseconds();
    ela=msa-ms;
    ms=msa;                                /*yyyymmddhhmissmis*/
    tim=translate('ij:kl:mn.opq',datetime(),'abcdefghijklmnopq');
    Put Edit(nn,' narcissistic:',j,ela,tim)
            (Skip,f(9),a,f(12),f(15),x(2),a(12));
    End;
  End;
dec2str: Proc(x) Returns(char(15) var);
Dcl x Dec Fixed(15);
Dcl ds Pic'(14)z9';
ds=x;
Return(trim(ds));
End;
milliseconds: Proc Returns(Dec Fixed(15));
Dcl c17 Char(17);
dcl 1 * Def C17,
     2 * char(8),
     2 hh Pic'99',
     2 mm Pic'99',
     2 ss Pic'99',
     2 ms Pic'999';
Dcl result Dec Fixed(15);
c17=datetime();
result=(((hh*60+mm)*60)+ss)*1000+ms;
Return(result);
End;
End;</lang>
Output:
        1 narcissistic:           0              0  00:41:43.632
        2 narcissistic:           1              0  00:41:43.632
        3 narcissistic:           2              0  00:41:43.632
        4 narcissistic:           3              0  00:41:43.632
        5 narcissistic:           4              0  00:41:43.632
        6 narcissistic:           5              0  00:41:43.632
        7 narcissistic:           6              0  00:41:43.632
        8 narcissistic:           7              0  00:41:43.632
        9 narcissistic:           8              0  00:41:43.632
       10 narcissistic:           9              0  00:41:43.632
       11 narcissistic:         153              0  00:41:43.632
       12 narcissistic:         370              0  00:41:43.632
       13 narcissistic:         371              0  00:41:43.632
       14 narcissistic:         407              0  00:41:43.632
       15 narcissistic:        1634              0  00:41:43.632
       16 narcissistic:        8208             20  00:41:43.652
       17 narcissistic:        9474             10  00:41:43.662
       18 narcissistic:       54748            130  00:41:43.792
       19 narcissistic:       92727            120  00:41:43.912
       20 narcissistic:       93084              0  00:41:43.912
       21 narcissistic:      548834           1310  00:41:45.222
       22 narcissistic:     1741725           3642  00:41:48.864
       23 narcissistic:     4210818           7488  00:41:56.352
       24 narcissistic:     9800817          22789  00:42:19.141
       25 narcissistic:     9926315            550  00:42:19.691
       26 narcissistic:    24678050          45358  00:43:05.049
       27 narcissistic:    24678051              0  00:43:05.049
       28 narcissistic:    88593477         237960  00:47:03.009
       29 narcissistic:   146511208         199768  00:50:22.777
       30 narcissistic:   472335975        1221384  01:10:44.161 

PowerShell

<lang PowerShell> function Test-Narcissistic ([int]$Number) {

   if ($Number -lt 0) {return $false}
   $total  = 0
   $digits = $Number.ToString().ToCharArray()
   foreach ($digit in $digits)
   {
       $total += [Math]::Pow([Char]::GetNumericValue($digit), $digits.Count)
   }
   $total -eq $Number

}


[int[]]$narcissisticNumbers = @() [int]$i = 0

while ($narcissisticNumbers.Count -lt 25) {

   if (Test-Narcissistic -Number $i)
   {
       $narcissisticNumbers += $i
   }
   $i++

}

$narcissisticNumbers | Format-Wide {"{0,7}" -f $_} -Column 5 -Force </lang>

Output:
      0                     1                     2                    3                    4
      5                     6                     7                    8                    9
    153                   370                   371                  407                 1634
   8208                  9474                 54748                92727                93084
 548834               1741725               4210818              9800817              9926315

Python

Procedural

This solution pre-computes the powers once.

<lang python>from __future__ import print_function from itertools import count, islice

def narcissists():

   for digits in count(0):
       digitpowers = [i**digits for i in range(10)]
       for n in range(int(10**(digits-1)), 10**digits):
           div, digitpsum = n, 0
           while div:
               div, mod = divmod(div, 10)
               digitpsum += digitpowers[mod]
           if n == digitpsum:
               yield n

for i, n in enumerate(islice(narcissists(), 25), 1):

   print(n, end=' ')
   if i % 5 == 0: print() 

print()</lang>

Output:
0 1 2 3 4 
5 6 7 8 9 
153 370 371 407 1634 
8208 9474 54748 92727 93084 
548834 1741725 4210818 9800817 9926315

Faster version:

Translation of: D

<lang python>try:

   import psyco
   psyco.full()

except:

   pass

class Narcissistics:

   def __init__(self, max_len):
       self.max_len = max_len
       self.power = [0] * 10
       self.dsum = [0] * (max_len + 1)
       self.count = [0] * 10
       self.len = 0
       self.ord0 = ord('0')
   def check_perm(self, out = [0] * 10):
       for i in xrange(10):
           out[i] = 0
       s = str(self.dsum[0])
       for d in s:
           c = ord(d) - self.ord0
           out[c] += 1
           if out[c] > self.count[c]:
               return
       if len(s) == self.len:
           print self.dsum[0],
   def narc2(self, pos, d):
       if not pos:
           self.check_perm()
           return
       while True:
           self.dsum[pos - 1] = self.dsum[pos] + self.power[d]
           self.count[d] += 1
           self.narc2(pos - 1, d)
           self.count[d] -= 1
           if d == 0:
               break
           d -= 1
   def show(self, n):
       self.len = n
       for i in xrange(len(self.power)):
           self.power[i] = i ** n
       self.dsum[n] = 0
       print "length %d:" % n,
       self.narc2(n, 9)
       print

def main():

   narc = Narcissistics(14)
   for i in xrange(1, narc.max_len + 1):
       narc.show(i)

main()</lang>

Output:
length 1: 9 8 7 6 5 4 3 2 1 0
length 2:
length 3: 407 371 370 153
length 4: 9474 8208 1634
length 5: 93084 92727 54748
length 6: 548834
length 7: 9926315 9800817 4210818 1741725
length 8: 88593477 24678051 24678050
length 9: 912985153 534494836 472335975 146511208
length 10: 4679307774
length 11: 94204591914 82693916578 49388550606 44708635679 42678290603 40028394225 32164049651 32164049650
length 12:
length 13:
length 14: 28116440335967

Functional

Translation of: Haskell
Translation of: JavaScript
Works with: Python version 3.7

<lang python>Narcissistic decimal numbers

from itertools import chain from functools import reduce


  1. main :: IO ()

def main():

   Narcissistic numbers of digit lengths 1 to 7
   print(
       fTable(main.__doc__ + ':\n')(str)(str)(
           narcissiOfLength
       )(enumFromTo(1)(7))
   )


  1. narcissiOfLength :: Int -> [Int]

def narcissiOfLength(n):

   List of Narcissistic numbers of
      (base 10) digit length n.
   
   return [
       x for x in digitPowerSums(n)
       if isDaffodil(n)(x)
   ]


  1. digitPowerSums :: Int -> [Int]

def digitPowerSums(e):

   The subset of integers of e digits that are potential narcissi.
      (Flattened leaves of a tree of unique digit combinations, in which
      order is not significant. The sum is independent of the sequence.)
   
   powers = [(x, x ** e) for x in enumFromTo(0)(9)]
   def go(n, parents):
       return go(
           n - 1,
           chain.from_iterable(map(
               lambda pDigitSum: (
                   map(
                       lambda lDigitSum: (
                           lDigitSum[0],
                           lDigitSum[1] + pDigitSum[1]
                       ),
                       powers[0: 1 + pDigitSum[0]]
                   )
               ),
               parents
           )) if parents else powers
       ) if 0 < n else parents
   return [xs for (_, xs) in go(e, [])]


  1. isDaffodil :: Int -> Int -> Bool

def isDaffodil(e):

   True if n is a narcissistic number
      of decimal digit length e.
   
   def go(n):
       ds = digitList(n)
       return e == len(ds) and n == powerSum(e)(ds)
   return lambda n: go(n)


  1. powerSum :: Int -> [Int] -> Int

def powerSum(e):

   The sum of a list obtained by raising
      each element of xs to the power of e.
   
   return lambda xs: reduce(
       lambda a, x: a + x ** e,
       xs, 0
   )


  1. -----------------------FORMATTING------------------------
  1. fTable :: String -> (a -> String) ->
  2. (b -> String) -> (a -> b) -> [a] -> String

def fTable(s):

   Heading -> x display function -> fx display function ->
      f -> xs -> tabular string.
   
   def go(xShow, fxShow, f, xs):
       ys = [xShow(x) for x in xs]
       w = max(map(len, ys))
       return s + '\n' + '\n'.join(map(
           lambda x, y: y.rjust(w, ' ') + ' -> ' + fxShow(f(x)),
           xs, ys
       ))
   return lambda xShow: lambda fxShow: lambda f: lambda xs: go(
       xShow, fxShow, f, xs
   )


  1. GENERIC -------------------------------------------------
  1. digitList :: Int -> [Int]

def digitList(n):

   A decomposition of n into a
      list of single-digit integers.
   
   def go(x):
       return go(x // 10) + [x % 10] if x else []
   return go(n) if n else [0]


  1. enumFromTo :: Int -> Int -> [Int]

def enumFromTo(m):

   Enumeration of integer values [m..n]
   def go(n):
       return list(range(m, 1 + n))
   return lambda n: go(n)


  1. MAIN ---

if __name__ == '__main__':

   main()</lang>
Output:
Narcissistic numbers of digit lengths 1 to 7:

1 -> [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
2 -> []
3 -> [153, 370, 371, 407]
4 -> [1634, 8208, 9474]
5 -> [54748, 92727, 93084]
6 -> [548834]
7 -> [1741725, 4210818, 9800817, 9926315]

Quackery

<lang Quackery> [ [] swap

   [ 10 /mod 
     rot join swap
     dup 0 = until ]
     drop ]                 is digits     ( n --> [   )
 [ dup digits
   0 over size rot
   witheach
     [ over ** rot + swap ]
   drop = ]                 is narcissistic ( n --> b )
 [] 0 
 [ dup narcissistic if
     [ tuck join swap ] 
   1+ over size 25 = until ]
 drop echo</lang>
Output:
[ 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 ]

R

For loop solution

This is a slow method and it needed above 5 minutes on a i3 machine. <lang rsplus>for (u in 1:10000000) { j <- nchar(u) set2 <- c() for (i in 1:j) { set2[i] <- as.numeric(substr(u, i, i)) } control <- c() for (k in 1:j) { control[k] <- set2[k]^(j) } if (sum(control) == u) print(u) }</lang>

Output:
[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 153
[1] 370
[1] 371
[1] 407
[1] 1634
[1] 8208
[1] 9474
[1] 54748
[1] 92727
[1] 93084
[1] 548834
[1] 1741725
[1] 4210818
[1] 9800817
[1] 9926315

While loop solution

As with the previous solution, this is rather slow. Regardless, we have made the following improvements:

  • This solution allows us to control how many Armstrong numbers we generate.
  • Rather than using a for loop that assumes that we will be done by the 10000000th case, we use a while loop.
  • Rather than using nchar or as.character, which both misbehave if the inputs are large enough for R to default to scientific notation, we use format.
  • We exploit many of R's vectorized functions, letting us avoid using any for loops.
  • As we are using format anyway, we take the chance to make the output look nicer.

<lang rsplus>generateArmstrong <- function(howMany) {

 resultCount <- i <- 0
 while(resultCount < howMany)
 {
   #The next line looks terrible, but I know of no better way to convert a large integer in to its digits in R.
   digits <- as.integer(unlist(strsplit(format(i, scientific = FALSE), "")))
   if(i == sum(digits^(length(digits)))) cat("Armstrong number ", resultCount <- resultCount + 1, ": ", format(i, big.mark = ","), "\n", sep = "")
   i <- i + 1
 } 

} generateArmstrong(25)</lang>

Output:
Armstrong number 1: 0
Armstrong number 2: 1
Armstrong number 3: 2
Armstrong number 4: 3
Armstrong number 5: 4
Armstrong number 6: 5
Armstrong number 7: 6
Armstrong number 8: 7
Armstrong number 9: 8
Armstrong number 10: 9
Armstrong number 11: 153
Armstrong number 12: 370
Armstrong number 13: 371
Armstrong number 14: 407
Armstrong number 15: 1,634
Armstrong number 16: 8,208
Armstrong number 17: 9,474
Armstrong number 18: 54,748
Armstrong number 19: 92,727
Armstrong number 20: 93,084
Armstrong number 21: 548,834
Armstrong number 22: 1,741,725
Armstrong number 23: 4,210,818
Armstrong number 24: 9,800,817
Armstrong number 25: 9,926,315

Racket

<lang racket>;; OEIS: A005188 defines these as positive numbers, so I will follow that definition in the function

definitions.
0
assuming it is represented as the single digit 0 (and not an empty string, which is not the
usual convention for 0 in decimal), is not
sum(0^0), which is 1. 0^0 is a strange one,
wolfram alpha calls returns 0^0 as indeterminate -- so I will defer to the brains behind OEIS
on the definition here, rather than copy what I'm seeing in some of the results here
  1. lang racket
Included for the serious efficientcy gains we get from fxvectors vs. general vectors.
We also use fx+/fx- etc. As it stands, they do a check for fixnumness, for safety.
We can link them in as "unsafe" operations (see the documentation on racket/fixnum);
but we get a result from this program quickly enough for my tastes.

(require racket/fixnum)

uses a precalculated (fx)vector of powers -- caller provided, please.

(define (sub-narcissitic? N powered-digits)

 (let loop ((n N) (target N))
   (cond
     [(fx> 0 target) #f]
     [(fx= 0 target) (fx= 0 n)]
     [(fx= 0 n) #f]
     [else (loop (fxquotient n 10)
                 (fx- target (fxvector-ref powered-digits (fxremainder n 10))))])))
Can be used as standalone, since it doesn't require caller to care about things like order of
magnitude etc. However, it *is* slow, since it regenerates the powered-digits vector every time.

(define (narcissitic? n) ; n is +ve

 (define oom+1 (fx+ 1 (order-of-magnitude n)))
 (define powered-digits (for/fxvector ((i 10)) (expt i oom+1)))
 (sub-narcissitic? n powered-digits))
next m primes > z

(define (next-narcissitics z m) ; naming convention following math/number-theory's next-primes

 (let-values
     ([(i l)
       (for*/fold ((i (fx+ 1 z)) (l empty))
         ((oom (in-naturals))
          (dgts^oom (in-value (for/fxvector ((i 10)) (expt i (add1 oom)))))
          (n (in-range (expt 10 oom) (expt 10 (add1 oom))))
          #:when (sub-narcissitic? n dgts^oom)
          ; everyone else uses ^C to break...
          ; that's a bit of a manual process, don't you think?
          #:final (= (fx+ 1 (length l)) m))
         (values (+ i 1) (append l (list n))))])
   l)) ; we only want the list

(module+ main

 (next-narcissitics 0 25)
 ; here's another list... depending on whether you believe sloane or wolfram :-)
 (cons 0 (next-narcissitics 0 25)))

(module+ test

 (require rackunit)
 ; example given at head of task  
 (check-true (narcissitic? 153))
 ; rip off the first 12 (and 0, since Armstrong numbers seem to be postivie) from
 ; http://oeis.org/A005188 for testing
 (check-equal?
  (for/list ((i (in-range 12))
             (n (sequence-filter narcissitic? (in-naturals 1)))) n)
  '(1 2 3 4 5 6 7 8 9 153 370 371))
 (check-equal? (next-narcissitics 0 12) '(1 2 3 4 5 6 7 8 9 153 370 371)))</lang>
Output:
(1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 24678050)
(0 1 2 ... 9926315)

Faster Version

This version uses lists of digits, rather than numbers themselves. <lang racket>#lang racket (define (non-decrementing-digital-sequences L)

 (define (inr d l)
   (cond
     [(<= l 0) '(())]
     [(= d 9) (list (make-list l d))]
     [else (append (map (curry cons d) (inr d (- l 1))) (inr (+ d 1) l))]))
 (inr 0 L))

(define (integer->digits-list n)

 (let inr ((n n) (l null)) (if (zero? n) l (inr (quotient n 10) (cons (modulo n 10) l)))))

(define (narcissitic-numbers-of-length L)

 (define tail-digits (non-decrementing-digital-sequences (sub1 L)))
 (define powers-v (for/fxvector #:length 10 ((i 10)) (expt i L)))
 (define (powers-sum dgts) (for/sum ((d (in-list dgts))) (fxvector-ref powers-v d)))
 (for*/list
     ((dgt1 (in-range 1 10))
      (dgt... (in-list tail-digits))
      (sum-dgt^l (in-value (powers-sum (cons dgt1 dgt...))))
      (dgts-sum (in-value (integer->digits-list sum-dgt^l)))
      #:when (= (car dgts-sum) dgt1)
      ; only now is it worth sorting the digits
      #:when (equal? (sort (cdr dgts-sum) <) dgt...))
   sum-dgt^l))

(define (narcissitic-numbers-of-length<= L)

 (cons 0 ; special!
       (apply append (for/list ((l (in-range 1 (+ L 1)))) (narcissitic-numbers-of-length l)))))

(module+ main

 (define all-narcissitics<10000000
   (narcissitic-numbers-of-length<= 7))
 ; conveniently, this *is* the list of 25... but I'll be a bit pedantic anyway
 (take all-narcissitics<10000000 25))

(module+ test

 (require rackunit)
 (check-equal? (non-decrementing-digital-sequences 1) '((0) (1) (2) (3) (4) (5) (6) (7) (8) (9)))
 (check-equal?
  (non-decrementing-digital-sequences 2)
  '((0 0) (0 1) (0 2) (0 3) (0 4) (0 5) (0 6) (0 7) (0 8) (0 9)
          (1 1) (1 2) (1 3) (1 4) (1 5) (1 6) (1 7) (1 8) (1 9)
          (2 2) (2 3) (2 4) (2 5) (2 6) (2 7) (2 8) (2 9)
          (3 3) (3 4) (3 5) (3 6) (3 7) (3 8) (3 9)
          (4 4) (4 5) (4 6) (4 7) (4 8) (4 9)
          (5 5) (5 6) (5 7) (5 8) (5 9) (6 6) (6 7) (6 8) (6 9)
          (7 7) (7 8) (7 9) (8 8) (8 9) (9 9)))
 
 (check-equal? (integer->digits-list 0) null)
 (check-equal? (integer->digits-list 7) '(7))
 (check-equal? (integer->digits-list 10) '(1 0))
 
 (check-equal? (narcissitic-numbers-of-length 1) '(1 2 3 4 5 6 7 8 9))
 (check-equal? (narcissitic-numbers-of-length 2) '())
 (check-equal? (narcissitic-numbers-of-length 3) '(153 370 371 407))
 
 (check-equal? (narcissitic-numbers-of-length<= 1) '(0 1 2 3 4 5 6 7 8 9))
 (check-equal? (narcissitic-numbers-of-length<= 3) '(0 1 2 3 4 5 6 7 8 9 153 370 371 407)))</lang>
Output:
'(0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 93084 92727 548834 1741725 4210818 9800817 9926315)

Raku

(formerly Perl 6) Here is a straightforward, naive implementation. It works but takes ages. <lang perl6>sub is-narcissistic(Int $n) { $n == [+] $n.comb »**» $n.chars }

for 0 .. * {

   if .&is-narcissistic {

.say; last if ++state$ >= 25;

   }

}</lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
Ctrl-C

Here the program was interrupted but if you're patient enough you'll see all the 25 numbers.

Here's a faster version that precalculates the values for base 1000 digits: <lang perl6>sub kigits($n) {

   my int $i = $n;
   my int $b = 1000;
   gather while $i {
       take $i % $b;
       $i = $i div $b;
   }

}

for (1..*) -> $d {

   my @t = 0..9 X** $d;
   my @table = @t X+ @t X+ @t;
   sub is-narcissistic(\n) { n == [+] @table[kigits(n)] };
   state $l = 2;
   FIRST say "1\t0";
   say $l++, "\t", $_ if .&is-narcissistic for 10**($d-1) ..^ 10**$d;
   last if $l > 25

};</lang>

Output:
1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	153
12	370
13	371
14	407
15	1634
16	8208
17	9474
18	54748
19	92727
20	93084
21	548834
22	1741725
23	4210818
24	9800817
25	9926315

REXX

idiomatic

<lang rexx>/*REXX program generates and displays a number of narcissistic (Armstrong) numbers. */ numeric digits 39 /*be able to handle largest Armstrong #*/ parse arg N . /*obtain optional argument from the CL.*/ if N== | N=="," then N=25 /*Not specified? Then use the default.*/ N=min(N, 89) /*there are only 89 narcissistic #s. */

  1. =0 /*number of narcissistic numbers so far*/
    do j=0  until #==N;     L=length(j)         /*get length of the  J  decimal number.*/
    $=left(j, 1) **L                            /*1st digit in  J  raised to the L pow.*/
              do k=2  for L-1  until $>j        /*perform for each decimal digit in  J.*/
              $=$ + substr(j, k, 1) ** L        /*add digit raised to power to the sum.*/
              end   /*k*/                       /* [↑]  calculate the rest of the sum. */
    if $\==j  then iterate                      /*does the sum equal to J?  No, skip it*/
    #=# + 1                                     /*bump count of narcissistic numbers.  */
    say right(#, 9)     ' narcissistic:'     j  /*display index and narcissistic number*/
    end   /*j*/                                 /*stick a fork in it,  we're all done. */</lang>
output   when using the default input:
        1  narcissistic: 0
        2  narcissistic: 1
        3  narcissistic: 2
        4  narcissistic: 3
        5  narcissistic: 4
        6  narcissistic: 5
        7  narcissistic: 6
        8  narcissistic: 7
        9  narcissistic: 8
       10  narcissistic: 9
       11  narcissistic: 153
       12  narcissistic: 370
       13  narcissistic: 371
       14  narcissistic: 407
       15  narcissistic: 1634
       16  narcissistic: 8208
       17  narcissistic: 9474
       18  narcissistic: 54748
       19  narcissistic: 92727
       20  narcissistic: 93084
       21  narcissistic: 548834
       22  narcissistic: 1741725
       23  narcissistic: 4210818
       24  narcissistic: 9800817
       25  narcissistic: 9926315 

optimized

This REXX version is optimized to pre-compute all the ten (single) digits raised to all possible powers (there are
only 39 possible widths/powers of narcissistic numbers).

It is about   77%   faster then 1st REXX version. <lang rexx>/*REXX program generates and displays a number of narcissistic (Armstrong) numbers. */ numeric digits 39 /*be able to handle largest Armstrong #*/ parse arg N . /*obtain optional argument from the CL.*/ if N== | N=="," then N=25 /*Not specified? Then use the default.*/ N=min(N, 89) /*there are only 89 narcissistic #s. */

    do     p=1  for 39                          /*generate tables:   digits ^ P power. */
        do i=0  for 10;      @.p.i= i**p        /*build table of ten digits ^ P power. */
        end   /*i*/
    end       /*w*/                             /* [↑]  table is a fixed (limited) size*/
  1. =0 /*number of narcissistic numbers so far*/
    do j=0  until #==N;      L=length(j)        /*get length of the  J  decimal number.*/
    _=left(j, 1)                                /*select the first decimal digit to sum*/
    $=@.L._                                     /*sum of the J dec. digits ^ L (so far)*/
              do k=2  for L-1  until $>j        /*perform for each decimal digit in  J.*/
              _=substr(j, k, 1)                 /*select the next decimal digit to sum.*/
              $=$ + @.L._                       /*add dec. digit raised to power to sum*/
              end   /*k*/                       /* [↑]  calculate the rest of the sum. */
    if $\==j  then iterate                      /*does the sum equal to J?  No, skip it*/
    #=# + 1                                     /*bump count of narcissistic numbers.  */
    say right(#, 9)     ' narcissistic:'     j  /*display index and narcissistic number*/
    end   /*j*/                                 /*stick a fork in it,  we're all done. */</lang>
output   is identical to the 1st REXX version.

optimized, unrolled

This REXX version is further optimized by unrolling part of the   do   loop that sums the decimal digits.

The unrolling also necessitated the special handling of one─ and two─digit narcissistic numbers.

It is about     44%   faster then 2nd REXX version,   and
it is about   154%   faster then 1st REXX version. <lang rexx>/*REXX program generates and displays a number of narcissistic (Armstrong) numbers. */ numeric digits 39 /*be able to handle largest Armstrong #*/ parse arg N . /*obtain optional argument from the CL.*/ if N== | N=="," then N=25 /*Not specified? Then use the default.*/ N=min(N, 89) /*there are only 89 narcissistic #s. */ @.=0 /*set default for the @ stemmed array. */

  1. =0 /*number of narcissistic numbers so far*/
    do p=0  for 39+1; if p<10  then call tell p /*display the 1st 1─digit dec. numbers.*/
        do i=1  for 9;     @.p.i= i**p          /*build table of ten digits ^ P power. */
        end   /*i*/
    end       /*p*/                             /* [↑]  table is a fixed (limited) size*/
                                                /* [↓]  skip the 2─digit dec. numbers. */
    do j=100;              L=length(j)          /*get length of the  J  decimal number.*/
    parse var  j    _1  2  _2  3  m    -1  _R /*get 1st, 2nd, middle, last dec. digit*/
    $=@.L._1  +  @.L._2  +  @.L._R              /*sum of the J decimal digs^L (so far).*/
             do k=3  for L-3  until $>j         /*perform for other decimal digits in J*/
             parse var  m    _  +1  m           /*get next dec. dig in J, start at 3rd.*/
             $=$ + @.L._                        /*add dec. digit raised to pow to sum. */
             end   /*k*/                        /* [↑]  calculate the rest of the sum. */
    if $==j  then do;  call tell j              /*does the sum equal to  J?  Show the #*/
                       if #==n  then leave      /*does the sum equal to  J?  Show the #*/
                  end
    end   /*j*/                                 /* [↑]  the  J loop  list starts at 100*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ tell: #=# + 1 /*bump the counter for narcissistic #s.*/

     say right(#,9)   ' narcissistic:'   arg(1) /*display index and narcissistic number*/
     if #==n  &  n<11  then exit                /*finished showing of narcissistic #'s?*/
     return                                     /*return to invoker & keep on truckin'.*/</lang>
output   is identical to the 1st REXX version.

optimized, 3-digit chunks

This REXX version is further optimized by pre-computing the narcissistic sums of all two-digit and three-digit numbers   (and also including those with leading zeros).

It is about     65%   faster then 3rd REXX version,   and
it is about   136%   faster then 2nd REXX version,   and
it is about   317%   faster then 1st REXX version. <lang rexx>/*REXX program generates and displays a number of narcissistic (Armstrong) numbers. */ numeric digits 39 /*be able to handle largest Armstrong #*/ parse arg N . /*obtain optional argument from the CL.*/ if N== | N=="," then N=25 /*Not specified? Then use the default.*/ N=min(N, 89) /*there are only 89 narcissistic #s. */ @.=0 /*set default for the @ stemmed array. */

  1. =0 /*number of narcissistic numbers so far*/
    do p=0  for 39+1; if p<10  then call tell p /*display the 1st 1─digit dec. numbers.*/
        do i=1  for 9;      @.p.i= i**p         /*build table of ten digits ^ P power. */
        zzj= '00'j;       @.p.zzj= @.p.j        /*assign value for a 3-dig number (LZ),*/
        end   /*i*/
        do j=10  to 99;   parse var j  t 2 u    /*obtain 2 decimal digits of J:    T U */
        @.p.j = @.p.t + @.p.u                   /*assign value for a 2─dig number.     */
        zj=  '0'j;        @.p.zj = @.p.j        /*   "     "    "  " 3─dig    "   (LZ),*/
        end   /*j*/                             /* [↑]  T≡ tens digit;  U≡ units digit.*/
        do k=100  to 999; parse var k h 2 t 3 u /*obtain 3 decimal digits of J:  H T U */
        @.p.k= @.p.h + @.p.t + @.p.u            /*assign value for a three-digit number*/
        end   /*k*/                             /* [↑]  H≡ hundreds digit;  T≡ tens ···*/
    end       /*p*/                             /* [↑]  table is a fixed (limited) size*/
                                                /* [↓]  skip the 2─digit dec. numbers. */
    do j=100;               L=length(j)         /*get length of the  J  decimal number.*/
    parse var  j  _  +3  m                      /*get 1st three decimal digits of  J.  */
    $=@.L._                                     /*sum of the J decimal digs^L (so far).*/
               do  while m\==                 /*do the rest of the dec. digs in  J.  */
               parse var  m    _  +3  m         /*get the next 3 decimal digits in  M. */
               $=$ + @.L._                      /*add dec. digit raised to pow to sum. */
               end   /*while*/                  /* [↑]  calculate the rest of the sum. */
    if $==j  then do;  call tell j              /*does the sum equal to  J?  Show the #*/
                       if #==n  then leave      /*does the sum equal to  J?  Show the #*/
                  end
    end   /*j*/                                 /* [↑]  the  J loop  list starts at 100*/

exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ tell: #=# + 1 /*bump the counter for narcissistic #s.*/

     say right(#,9)   ' narcissistic:'   arg(1) /*display index and narcissistic number*/
     if #==n  &  n<11  then exit                /*finished showing of narcissistic #'s?*/
     return                                     /*return to invoker & keep on truckin'.*/</lang>
output   is identical to the 1st REXX version.

Further optimization could be utilized by increasing the chunk size to four or five decimal digits,
but with an accompanying increase in the size of the pre-computed values.

Ring

<lang ring> n = 0 count = 0 size = 15 while count != size

     m = isNarc(n)
     if m=1 see "" + n + " is narcisstic" + nl 
        count = count + 1 ok
     n = n + 1 

end

func isNarc n

    m = len(string(n))
    sum = 0
    digit = 0
    for pos = 1 to m
        digit = number(substr(string(n), pos, 1))
        sum = sum + pow(digit,m)
    next
    nr = (sum = n)
    return nr

</lang>

Ruby

<lang ruby>class Integer

 def narcissistic?
   return false if negative?
   digs = self.digits    
   m    = digs.size
   digs.map{|d| d**m}.sum == self
 end

end

puts 0.step.lazy.select(&:narcissistic?).first(25)</lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315

Rust

<lang rust> fn is_narcissistic(x: u32) -> bool {

   let digits: Vec<u32> = x
       .to_string()
       .chars()
       .map(|c| c.to_digit(10).unwrap())
       .collect();
   digits
       .iter()
       .map(|d| d.pow(digits.len() as u32))
       .sum::<u32>()
       == x

}

fn main() {

   let mut counter = 0;
   let mut i = 0;
   while counter < 25 {
       if is_narcissistic(i) {
           println!("{}", i);
           counter += 1;
       }
       i += 1;
   }

} </lang>

Output:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315

Scala

Works with: Scala version 2.9.x

<lang Scala>object NDN extends App {

 val narc: Int => Int = n => (n.toString map (_.asDigit) map (math.pow(_, n.toString.size)) sum) toInt
 val isNarc: Int => Boolean = i => i == narc(i)
 println((Iterator from 0 filter isNarc take 25 toList) mkString(" "))

}</lang>

Output:

0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315

Sidef

<lang ruby>func is_narcissistic(n) {

   n.digits »**» n.len -> sum == n

}   var count = 0 for i in ^Inf {

   if (is_narcissistic(i)) {
       say "#{++count}\t#{i}"
       break if (count == 25)
   }

}</lang>

Output:
1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	153
12	370
13	371
14	407
15	1634
16	8208
17	9474
18	54748
19	92727
20	93084
21	548834
22	1741725
23	4210818
24	9800817
25	9926315

Swift

<lang swift>extension BinaryInteger {

 @inlinable
 public var isNarcissistic: Bool {
   let digits = String(self).map({ Int(String($0))! })
   let m = digits.count
   guard m != 1 else {
     return true
   }
   return digits.map({ $0.power(m) }).reduce(0, +) == self
 }
 @inlinable
 public func power(_ n: Self) -> Self {
   return stride(from: 0, to: n, by: 1).lazy.map({_ in self }).reduce(1, *)
 }

}

let narcs = Array((0...).lazy.filter({ $0.isNarcissistic }).prefix(25))

print("First 25 narcissistic numbers are \(narcs)")</lang>

Output:
First 25 narcissistic numbers are [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315]

Tcl

<lang tcl>proc isNarcissistic {n} {

   set m [string length $n]
   for {set t 0; set N $n} {$N} {set N [expr {$N / 10}]} {

incr t [expr {($N%10) ** $m}]

   }
   return [expr {$n == $t}]

}

proc firstNarcissists {target} {

   for {set n 0; set count 0} {$count < $target} {incr n} {

if {[isNarcissistic $n]} { incr count lappend narcissists $n }

   }
   return $narcissists

}

puts [join [firstNarcissists 25] ","]</lang>

Output:
0,1,2,3,4,5,6,7,8,9,153,370,371,407,1634,8208,9474,54748,92727,93084,548834,1741725,4210818,9800817,9926315

UNIX Shell

Works with: ksh93

<lang bash>function narcissistic {

   integer n=$1 len=${#n} sum=0 i
   for ((i=0; i<len; i++)); do
       (( sum += pow(${n:i:1}, len) ))
   done
   (( sum == n ))

}

nums=() for ((n=0; ${#nums[@]} < 25; n++)); do

   narcissistic $n && nums+=($n)

done echo "${nums[*]}" echo "elapsed: $SECONDS"</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315
elapsed: 436.639

VBA

Translation of: Phix
<lang vb>Private Function narcissistic(n As Long) As Boolean
   Dim d As String: d = CStr(n)
   Dim l As Integer: l = Len(d)
   Dim sumn As Long: sumn = 0
   For i = 1 To l
       sumn = sumn + (Mid(d, i, 1) - "0") ^ l
   Next i
   narcissistic = sumn = n

End Function

Public Sub main()

   Dim s(24) As String
   Dim n As Long: n = 0
   Dim found As Integer: found = 0
   Do While found < 25
       If narcissistic(n) Then
           s(found) = CStr(n)
           found = found + 1
       End If
       n = n + 1
   Loop
   Debug.Print Join(s, ", ")
End Sub</lang>
Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315

VBScript

<lang vb>Function Narcissist(n) i = 0 j = 0 Do Until j = n sum = 0 For k = 1 To Len(i) sum = sum + CInt(Mid(i,k,1)) ^ Len(i) Next If i = sum Then Narcissist = Narcissist & i & ", " j = j + 1 End If i = i + 1 Loop End Function

WScript.StdOut.Write Narcissist(25)</lang>

Output:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315,

Wren

Translation of: Go

<lang ecmascript>var narc = Fn.new { |n|

   var power = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
   var limit = 10
   var result = []
   var x = 0
   while (result.count < n) {
       if (x >= limit) {
           for (i in 0..9) power[i] = power[i] * i
           limit = limit * 10
       }
       var sum = 0
       var xx = x
       while (xx > 0) {
           sum = sum + power[xx%10]
           xx = (xx/10).floor
       }
       if (sum == x) result.add(x)
       x = x + 1
   }
   return result

}

System.print(narc.call(25))</lang>

Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 153, 370, 371, 407, 1634, 8208, 9474, 54748, 92727, 93084, 548834, 1741725, 4210818, 9800817, 9926315]

XPL0

This is based on Ring's version for Own Digits Power Sum. <lang XPL0>func IPow(A, B); \A^B int A, B, T, I; [T:= 1; for I:= 1 to B do T:= T*A; return T; ];

int Count, M, N, Sum, T, Dig; [Text(0, "0 "); Count:= 1; for M:= 1 to 9 do

   for N:= IPow(10, M-1) to IPow(10, M)-1 do
       [Sum:= 0;
       T:= N;
       while T do
           [T:= T/10;
           Dig:= rem(0);
           Sum:= Sum + IPow(Dig, M);
           ];
       if Sum = N then
           [IntOut(0, N);  ChOut(0, ^ );
           Count:= Count+1;
           if Count >= 25 then exit;
           ];
       ];

]</lang>

Output:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 

zkl

<lang zkl>fcn isNarcissistic(n){

  ns,m := n.split(), ns.len() - 1;
  ns.reduce('wrap(s,d){ z:=d; do(m){z*=d} s+z },0) == n

}</lang> Pre computing the first 15 powers of 0..9 for use as a look up table speeds things up quite a bit but performance is pretty underwhelming. <lang zkl>var [const] powers=(10).pump(List,'wrap(n){

     (1).pump(15,List,'wrap(p){ n.toFloat().pow(p).toInt() }) });

fcn isNarcissistic2(n){

  m:=(n.numDigits - 1);
  n.split().reduce('wrap(s,d){ s + powers[d][m] },0) == n

}</lang> Now stick a filter on a infinite lazy sequence (ie iterator) to create an infinite sequence of narcissistic numbers (iterator.filter(n,f) --> n results of f(i).toBool()==True). <lang zkl>ns:=[0..].filter.fp1(isNarcissistic); ns(15).println(); ns(5).println(); ns(5).println();</lang>

Output:
L(0,1,2,3,4,5,6,7,8,9,153,370,371,407,1634)
L(8208,9474,54748,92727,93084)
L(548834,1741725,4210818,9800817,9926315)

ZX Spectrum Basic

Array index starts at 1. Only 1 character long variable names are allowed for For-Next loops. 8 Digits or higher numbers are displayed as floating point numbers. Needs about 2 hours (3.5Mhz) <lang zxbasic> 1 DIM K(10): DIM M(10)

2 FOR Y=0 TO 9: LET M(Y+1)=Y: NEXT Y
3 FOR N=1 TO 7
4 FOR J=N TO 0 STEP -1
5 FOR I=N-J TO 0 STEP -1
6 FOR H=N-J-I TO 0 STEP -1
7 FOR G=N-J-I-H TO 0 STEP -1
8 FOR F=N-J-I-H-G TO 0 STEP -1
9 FOR E=N-J-I-H-G-F TO 0 STEP -1

10 FOR D=N-J-I-H-G-F-E TO 0 STEP -1 11 FOR C=N-J-I-H-G-F-E-D TO 0 STEP -1 12 FOR B=N-J-I-H-G-F-E-D-C TO 0 STEP -1 13 LET A=N-J-I-H-G-F-E-D-C-B 14 LET X=B+C*M(3)+D*M(4)+E*M(5)+F*M(6)+G*M(7)+H*M(8)+I*M(9)+J*M(10) 15 LET S$=STR$ (X) 16 IF LEN (S$)<N THEN GO TO 34 17 IF LEN (S$)<>N THEN GO TO 33 18 FOR Y=1 TO 10: LET K(Y)=0: NEXT Y 19 FOR Y=1 TO N 20 LET Z= CODE (S$(Y))-47 21 LET K(Z)=K(Z)+1 22 NEXT Y 23 IF A<>K(1) THEN GO TO 33 24 IF B<>K(2) THEN GO TO 33 25 IF C<>K(3) THEN GO TO 33 26 IF D<>K(4) THEN GO TO 33 27 IF E<>K(5) THEN GO TO 33 28 IF F<>K(6) THEN GO TO 33 29 IF G<>K(7) THEN GO TO 33 30 IF H<>K(8) THEN GO TO 33 31 IF I<>K(9) THEN GO TO 33 32 IF J=K(10) THEN PRINT X, 33 NEXT B: NEXT C: NEXT D: NEXT E: NEXT F: NEXT G: NEXT H: NEXT I: NEXT J 34 FOR Y=2 TO 9 35 LET M(Y+1)=M(Y+1)*Y 36 NEXT Y 37 NEXT N 38 PRINT 39 PRINT "DONE"</lang>

Output:
9               8
7               6
5               4
3               2
1               0
9               8
7               6
5               4
3               2
1               0
407             371
370             153
9474            8208
1634            93084
92727           54748
548834          9926315
9800817         4210818
1741725