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A Narcissistic decimal number is a non-negative integer, $n$ in which if there are $m$ digits in its decimal representation then the sum of all the individual digits of the decimal representation raised to the power $m$ is equal to $n$ .

For example, if $n$ is 153 then $m$ , the number of digits is 3 and we have $1^{3}+5^{3}+3^{3}=1+125+27=153$ and so 153 is a narcissistic decimal integer number.

The task is to generate and show here, the first 25 narcissistic integer numbers.

Note: $0^{1}=0$ , the first in the series.

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

AutoHotkey

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

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

C

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

include <gmp.h>

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++

include <iostream>
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

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:

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.

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:

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]

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]

Haskell

<lang Haskell>import System.IO

digits :: (Read a, Show a) => a -> [a] digits n = map (read . (:[])) $ show n

isNarcissistic :: (Show a, Read a, Num a, Eq a) => a -> Bool isNarcissistic n =

 let dig = digits n
     len = length dig
 in n == (sum $ map (^ len) $ dig)

main :: IO () main = do

 hSetBuffering stdout NoBuffering
 putStrLn $ unwords $ map show $ take 25 $ filter isNarcissistic [(0 :: Int)..]</lang>

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:

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

JavaScript

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"

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

Oforth

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

  n 0 while(n 0 <>) [ n 10 divrem ->n swap 1 + ] ->m
  0 m loop: i [ swap m pow asInteger + ]
  ==

}

func: genNarcissistic { | l |

  ListBuffer new ->l
  0 while(l size 25 <>) [ dup isNarcissistic ifTrue: [ dup l add ] 1 + ]
  drop l println

}</lang>

Output:

>genNarcissistic
[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]

Pascal

Works with: 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

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>

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:

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;
   }

}

constant narcissistic = 0, (1..*).map: -> $d {

   my @t = 0..9 X** $d;
   my @table = @t X+ @t X+ @t;
   sub is-narcissistic(\n) { n == [+] @table[kigits(n)] }
   gather take $_ if is-narcissistic($_) for 10**($d-1) ..^ 10**$d;

}

for narcissistic {

   say ++state $n, "\t", $_;
   last if $n == 25;

}</lang>

Output:

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

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

Python

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

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

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)

REXX

idomatic

<lang rexx>/*REXX program to generate and display a number of narcissistic numbers.*/ numeric digits 39 /*be able to handle the largest #*/ parse arg N .; if N== then N=25 /*get number of narcissistic #'s.*/ N=min(N,89) /*there are 89 narcissistic #s.*/

=0 /*number of narcissistic # so far*/

    do j=0  until #==N;   L=length(j) /*get the length of the J number.*/
    s=left(j,1)**L                    /*1st digit in J raised to L pow.*/
           do k=2  for L-1  until s>j /*perform for each digit in  J.  */
           s=s + substr(j,k,1)**L     /*add digit raised to pow to sum.*/
           end   /*k*/                /* [↑]  calculate the rest of sum*/
    if s\==j  then iterate            /*does sum equal to  J?   No ··· */
    #=#+1                             /*bump the narcissistic num count*/
    say right(#,9) ' narcissistic:' j /*display index & narcissistic #.*/
    end   /*j*/                       /* [↑]    this list starts at 0. */
                                      /*stick a fork in it, we're 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 (which is 39). <lang rexx>/*REXX program to generate and display a number of narcissistic numbers.*/ numeric digits 39 /*be able to handle the largest #*/ parse arg N .; if N== then N=25 /*get number of narcissistic #'s.*/ N=min(N,89) /*there are 89 narcissistic #s.*/

  do w=1  for 39                      /*generate tables: digits ^ L pow*/
    do i=0  for 10;  @.w.i=i**w;  end /*build table of 10 digs ^ L pow.*/
  end   /*w*/                         /* [↑]  table is of a fixed size.*/

=0 /*number of narcissistic # so far*/

    do j=0  until #==N;   L=length(j) /*get the length of the J number.*/
    _=left(j,1)                       /*select the first digit to sum. */
    s=@.L._                           /*sum of the J digs ^ L  (so far)*/
            do k=2  for L-1 until s>j /*perform for each digit in  J.  */
            _=substr(j,k,1)           /*select the next digit to sum.  */
            s=s+@.L._                 /*add digit raised to pow to sum.*/
            end   /*k*/               /* [↑]  calculate the rest of sum*/
    if s\==j  then iterate            /*does sum equal to  J?   No ··· */
    #=#+1                             /*bump the narcissistic num count*/
    say right(#,9) ' narcissistic:' j /*display index & narcissistic #.*/
    end   /*j*/                       /* [↑]    this list starts at 0. */
                                      /*stick a fork in it, we're done.*/</lang>

output is the same as 1st REXX version.

optimized, unrolled

This REXX version is optimized by unrolling part of the DO loop that sums the digits.
The unrolling also necessitated the special handling of one- and two-digit narcissistic numbers. <lang rexx>/*REXX program to generate and display a number of narcissistic numbers.*/ numeric digits 39 /*be able to handle the largest #*/ parse arg N .; if N== then N=25 /*get number of narcissistic #'s.*/ N=min(N,89) /*there are 89 narcissistic #s.*/

  do w=1  for 39                      /*generate tables: digits ^ L pow*/
    do i=0  for 10;  @.w.i=i**w;  end /*build table of 10 digs ^ L pow.*/
  end   /*w*/                         /* [↑]  table is of a fixed size.*/

=0 /*number of narcissistic # so far*/

  do low=0 for 10; call tell low; end /*handle the first one-digit nums*/
                                      /* [↓]  skip the 2-digit numbers.*/
    do j=100;      L=length(j)        /*get the length of the J number.*/
    _1=left(j,1); _2=substr(j,2,1)    /*select 1st & 2nd digit to sum. */
    _R=right(j,1)                     /*select the right digit to sum. */
    s=@.L._1 + @.L._2 + @.L._R        /*sum of the J digs ^ L  (so far)*/
            do k=3  for L-3 until s>j /*perform for each digit in  J.  */
            _=substr(j,k,1)           /*select the next digit to sum.  */
            s=s + @.L._               /*add digit raised to pow to sum.*/
            end   /*k*/               /* [↑]  calculate the rest of sum*/
    if s==j  then call tell j         /*does sum equal to  J?   Yes ···*/
    end   /*j*/                       /* [↑]    this list starts at 0. */

exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────TELL subroutine─────────────────────*/ tell: parse arg y /*get narcissistic # to display. */

=#+1 /*bump the narcissistic # count. */

say right(#,9) ' narcissistic:' y /*display index & narcissistic #.*/ if #==N then exit /*stick a fork in it, we're done.*/ return /*return and keep on truckin'. */</lang> output is the same as 1st REXX version.

Ruby

<lang ruby>class Integer

 def narcissistic?
   return false if self < 0
   len = to_s.size
   n = self
   sum = 0
   while n > 0
     n, r = n.divmod(10)
     sum += r ** len
   end
   sum == self
 end

end

numbers = [] n = 0 while numbers.size < 25

 numbers << n if n.narcissistic?
 n += 1

end

or
numbers = 0.step.lazy.select(&:narcissistic?).first(25) # Ruby ver 2.1

max = numbers.max.to_s.size g = numbers.group_by{|n| n.to_s.size} g.default = [] (1..max).each{|n| puts "length #{n} : #{g[n].join(", ")}"}</lang>

Output:

length 1 : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
length 2 : 
length 3 : 153, 370, 371, 407
length 4 : 1634, 8208, 9474
length 5 : 54748, 92727, 93084
length 6 : 548834
length 7 : 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

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

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,

zkl

<lang zkl>fcn isNarcissistic(n){

  ns:=n.split();
  m:=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 powers=(10).pump(List,'wrap(n){

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

fcn isNarcissistic(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)