Narcissistic decimal number

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,   ${\displaystyle n}$,   that is equal to the sum of the   ${\displaystyle m}$-th   powers of each of the digits in the decimal representation of   ${\displaystyle n}$,   where   ${\displaystyle m}$   is the number of digits in the decimal representation of   ${\displaystyle n}$.

Narcissistic (decimal) numbers are sometimes called   Armstrong   numbers, named after Michael F. Armstrong.

An example

•   if   ${\displaystyle n}$   is   153
•   then   ${\displaystyle m}$,   (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:   ${\displaystyle 0^{1}=0}$,   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

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

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

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 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

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

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
     LENG=LEN(MID$(STR$(N),2))
     SUM=0
     FOR I=1 TO LENG DO
       C$=MID$(STR$(N),2)
       C=VAL(MID$(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

FreeBASIC

Simple Version

<lang FreeBASIC>' normal version: 17-06-2015 ' compile with: fbc -s console ' can go up to 19 digits (ulongint is 64bit), above 19 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*d2pow(1) + 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 <> "" : Var _key_ = 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 <> "" : Var _key_ = InKey : Wend Print : Print "hit any key to end program" Sleep End</lang>

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:

->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

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"

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> function isnarcissist{T<:Integer}(n::T, b::Int=10)

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

end

goal = 25 ncnt = 0 println("Finding the first ", goal, " Narcissistic numbers:") for i in 0:typemax(1)

   isnarcissist(i) || continue
   ncnt += 1
   println(@sprintf "    %2d %7d" ncnt i)
   ncnt < goal || break

end </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

Mathematica

<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

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

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:

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;
   }

}

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:

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

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

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

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)

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 .; if N== | N=="," then N=25 /*obtain the number of narcissistic #'s*/ 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*/                                 /* [↑]    this list starts at 0 (zero).*/
                                                /*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). <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 .; if N== | N=="," then N=25 /*obtain the number of narcissistic #'s*/ N=min(N, 89) /*there are only 89 narcissistic #s. */

    do     w=1  for 39                          /*generate tables:   digits ^ L power. */
        do i=0  for 10;      @.w.i=i**w         /*build table of ten digits ^ L 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*/                                 /* [↑]    this list starts at 0 (zero).*/
                                                /*stick a fork in it,  we're all done. */</lang>

output   is the same as 1^st REXX version.

optimized, unrolled

This REXX version is further 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 generates and displays a number of narcissistic (Armstrong) numbers. */ numeric digits 39 /*be able to handle largest Armstrong #*/ parse arg N .; if N== | N=="," then N=25 /*obtain the number of narcissistic #'s*/ 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 w=0  for 39+1; if w<10  then call tell w /*display the 1st 1─digit dec. numbers.*/
        do i=1  for 9;    @.w.i=i**w            /*build table of ten digits ^ L power. */
        end   /*i*/
    end       /*w*/                             /* [↑]  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 call tell j                   /*does the sum equal to  J?  Show the #*/
    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  then exit                         /*stick a fork in it,  we're all done. */
     return                                     /*return to invoker & keep on truckin'.*/</lang>

output   is the same as 1^st REXX version.

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 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

1. or
2. 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

Sidef

<lang ruby>func is_narcissistic(n) {

   n.digits »**» n.len -> sum(0) == n

}

var count = 0 for i in (0..^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

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)