# Narcissistic decimal number

(Redirected from Armstrong numbers)
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.
They are also known as   Plus Perfect   numbers.

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

Generate and show here the first   25   narcissistic decimal numbers.

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

## 11l

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

L(n) narcissists(25)
print(n, end' ‘ ’)
I (L.index + 1) % 5 == 0
print()```
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
```

```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
Count := Count + 1;
end if;
Current := Current + 1;
end loop;
end Narcissistic;
```
Output:
` 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315`

## Agena

Tested with Agena 2.9.5 Win32

```scope
# print the first 25 narcissistic numbers

local power := reg( 0, 1, 1, 1, 1, 1, 1, 1, 1, 1 );
local count      := 0;
local maxCount   := 25;
local candidate  := 0;
local prevDigits := 0;
local digits     := 1;

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

epocs```
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

```# find some narcissistic decimal numbers                                      #

# 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 # ;

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

## ALGOL W

Translation of: Agena
```begin
% print the first 25 narcissistic numbers                                 %

integer array  power( 0 :: 9 );
integer count, candidate, prevDigits, digits;

power( 0 ) := 0;
for i := 1 until 9 do power( i ) := 1;

count      := 0;
candidate  := 0;
prevDigits := 0;
digits     := 1;

for d9 := 0 until 2 do begin
if d9 > 0 and digits < 9 then digits := 9;
for d8 := 0 until 9 do begin
if d8 > 0 and digits < 8 then digits := 8;
for d7 := 0 until 9 do begin
if d7 > 0 and digits < 7 then digits := 7;
for d6 := 0 until 9 do begin
if d6 > 0 and digits < 6 then digits := 6;
for d5 := 0 until 9 do begin
if d5 > 0 and digits < 5 then digits := 5;
for d4 := 0 until 9 do begin
if d4 > 0 and digits < 4 then digits := 4;
for d3 := 0 until 9 do begin
if d3 > 0 and digits < 3 then digits := 3;
for d2 := 0 until 9 do begin
if d2 > 0 and digits < 2 then digits := 2;
for d1 := 0 until 9 do begin
integer number, sum;
if prevDigits <> digits then begin
% number of digits has increased %
% - increase the powers          %
prevDigits := digits;
for i := 2 until 9 do power( i ) := power( i ) * i;
end;

% sum the digits'th powers of the    %
% digits of candidate                %
sum := power( d1 ) + power( d2 ) + power( d3 )
+ power( d4 ) + power( d5 ) + power( d6 )
+ power( d7 ) + power( d8 ) + power( d9 )
;
if candidate = sum then begin
% found another narcissistic    %
% decimal number                %
writeon( i_w := 1, s_w := 1, candidate );
count := count + 1;
if count >= 25 then goto done
end;
candidate := candidate + 1
end d1;
end d2;
end d3;
end d4;
end d5;
end d6;
end d7;
end d8;
end d9;
done:
write()

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

## APL

```∇r ← digitsOf n;digitList
digitList ← ⍬
loop:→((⌊n)=0)/done
digitList ← digitList,(⌊n|⍨10)
n ← n÷10
→loop
done: r ← ⊖digitList
∇

∇r ← getASN n;idx;list
idx ← 0
list ← 0⍴0
loop:
→(n=⍴list)/done
→next
list ← list,idx
next:
idx ← idx+1
→loop
done:
r ← list
∇

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

getASN 25
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315
```

## AppleScript

### Functional

Translation of: JavaScript

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

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

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

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

```------------------------- NARCISSI -----------------------

-- isDaffodil :: Int -> Int -> Bool
on isDaffodil(e, n)
set ds to digitList(n)
(e = length of ds) and (n = powerSum(e, ds))
end isDaffodil

-- digitList :: Int -> [Int]
on digitList(n)
if n > 0 then
{n mod 10} & digitList(n div 10)
else
{}
end if
end digitList

-- powerSum :: Int -> [Int] -> Int
on powerSum(e, ns)
script
on |λ|(a, x)
a + x ^ e
end |λ|
end script

foldl(result, 0, ns) as integer
end powerSum

-- narcissiOfLength :: Int -> [Int]
on narcissiOfLength(nDigits)
script nthPower
on |λ|(x)
{x, x ^ nDigits as integer}
end |λ|
end script
set powers to map(nthPower, enumFromTo(0, 9))

script combn
on digitTree(n, parents)
if n > 0 then
if parents ≠ {} then
script nextLayer
on |λ|(pair)
set {digit, intSum} to pair
on |λ|(dp)
set {d, p} to dp
{d, p + intSum}
end |λ|
end script

map(addPower, items 1 thru (digit + 1) of powers)
end |λ|
end script

set nodes to concatMap(nextLayer, parents)
else
set nodes to powers
end if
digitTree(n - 1, nodes)
else
script
on |λ|(pair)
isDaffodil(nDigits, item 2 of pair)
end |λ|
end script

filter(result, parents)
end if
end digitTree
end script

script snd
on |λ|(ab)
item 2 of ab
end |λ|
end script
map(snd, combn's digitTree(nDigits, {}))
end narcissiOfLength

--------------------------- TEST -------------------------
on run

{0} & concatMap(narcissiOfLength, enumFromTo(1, 5))
-- 4 seconds, 20 narcissi

-- {0} & concatMap(narcissiOfLength, enumFromTo(1, 6))
-- 103 seconds, 21 narcissi

-- {0} & concatMap(narcissiOfLength, enumFromTo(1, 7))
-- 13.75 minutes, 25 narcissi

end run

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

-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set lst to {}
set lng to length of xs
tell mReturn(f)
repeat with i from 1 to lng
set lst to (lst & |λ|(item i of xs, i, xs))
end repeat
end tell
return lst
end concatMap

-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if n < m then
set d to -1
else
set d to 1
end if
set lst to {}
repeat with i from m to n by d
set end of lst to i
end repeat
return lst
end enumFromTo

-- filter :: (a -> Bool) -> [a] -> [a]
on filter(f, xs)
tell mReturn(f)
set lst to {}
set lng to length of xs
repeat with i from 1 to lng
set v to item i of xs
if |λ|(v, i, xs) then set end of lst to v
end repeat
return lst
end tell
end filter

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
```
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}
```

### Idiomatic

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

```(*
Return the first q narcissistic decimal numbers
(or as many of the q as can be represented by AppleScript number values).
*)
on narcissisticDecimalNumbers(q)
script o
property output : {}
property listOfDigits : missing value
property m : 0 -- Digits per collection/number.
property done : false

-- Recursive subhandler. Builds lists containing m digit values while summing the digits' mth powers.
on recurse(digitList, sumOfPowers, digitShortfall)
-- If m digits have been obtained, compare the sum of powers's digits with the values in the list.
-- Otherwise continue branching the recursion to derive longer lists.
if (digitShortfall is 0) then
-- Assign the list to a script property to allow faster references to its items (ie. incl. reference to script).
set listOfDigits to digitList
set temp to sumOfPowers
set unmatched to m
repeat until (temp = 0)
set sumDigit to temp mod 10
if (sumDigit is in digitList) then
repeat with d from 1 to unmatched
if (sumDigit = number d of my listOfDigits) then
set number d of my listOfDigits to missing value
set unmatched to unmatched - 1
exit repeat
end if
end repeat
else
exit repeat
end if
set temp to temp div 10
end repeat
-- If all the digits have been matched, the sum of powers is narcissistic.
if (unmatched is 0) then
set end of my output to sumOfPowers div 1
-- If it's the qth find, signal the end of the process.
if ((count my output) = q) then set done to true
end if
else
-- If fewer than m digits at this level, derive longer lists from the current one.
-- Adding only values that are less than or equal to the last one makes each
-- collection unique and turns up the narcissistic numbers in numerical order.
repeat with additionalDigit from 0 to end of digitList
if (done) then exit repeat
end repeat
end if
end recurse
end script

(* Rest of main handler code. *)
if (q > 89) then set q to 89 -- Number of narcissistic decimal integers known to exist.
set maxM to 16 -- Maximum number of decimal digits (other than trailing zeros) in AppleScript numbers.
tell o
-- Begin with zero, which is narcissistic by definition and is never the only digit used in other numbers.
if (q > 0) then set end of its output to 0
if (q < 2) then set its done to true
-- Initiate the recursive building and testing of collections of increasing numbers of digit values.
repeat until (its done)
set its m to (its m) + 1
if (its m > maxM) then
set end of its output to "Remaining numbers beyond AppleScript's number precision"
set its done to true
else
repeat with digit from 1 to 9
recurse({digit}, digit ^ (its m), (its m) - 1)
if (its done) then exit repeat
end repeat
end if
end repeat

return its output
end tell
end narcissisticDecimalNumbers

return narcissisticDecimalNumbers(25)
```
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}
```

## Arturo

Translation of: REXX
```powers: map 0..9 'x [
map 0..9 'y [
x ^ y
]
]

getPair: function [p,sz].memoize[
if not? numeric? last p -> return powers\[to :integer to :string first p]\[sz]
return powers\[to :integer to :string first p]\[sz] + powers\[to :integer to :string last p]\[sz]
]

narcissistic?: function [n][
digs: digits n
sdigs: size digs
n = sum map split.every:2 to :string n 'p -> getPair p sdigs
]

i: new 0
counter: new 0
while [counter < 25][
if narcissistic? i [
print i
inc 'counter
]
inc 'i
]
```
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
}
}
}
```
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)
}
```

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
```

## BASIC

### Chipmunk Basic

Translation of: Go

Differently from the original version, no data structure for the result is used - why should it be?

```100 rem Narcissistic decimal number
110 n = 25
120 dim power(9)
130 for i = 0 to 9
140   power(i) = i
150 next i
160 limit = 10
170 cnt = 0 : x = 0
180 while cnt < n
190   if x >= limit then
200     for i = 0 to 9
210         power(i) = power(i)*i
220     next i
230     limit = limit*10
240   endif
250   sum = 0 : xx = x
260   while xx > 0
270     sum = sum+power(xx mod 10)
280     xx = int(xx/10)
290   wend
300   if sum = x then print x; : cnt = cnt+1
310   x = x+1
320 wend
330 print
340 end
```
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

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

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

For n = 1 To 7
For n9 = n To 0 Step -1
For n8 = n-n9 To 0 Step -1
For n7 = n-n9-n8 To 0 Step -1
For n6 = n-n9-n8-n7 To 0 Step -1
For n5 = n-n9-n8-n7-n6 To 0 Step -1
For n4 = n-n9-n8-n7-n6-n5 To 0 Step -1
For n3 = n-n9-n8-n7-n6-n5-n4 To 0 Step -1
For n2 = n-n9-n8-n7-n6-n5-n4-n3 To 0 Step -1
For n1 = n-n9-n8-n7-n6-n5-n4-n3-n2 To 0 Step -1
n0 = n-n9-n8-n7-n6-n5-n4-n3-n2-n1

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

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

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

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

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

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

Next n

' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
```
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.```
```' gmp version: 17-06-2015
' uses gmp
' compile with: fbc -s console

#Include Once "gmp.bi"
' change the number after max for the maximum n-digits you want (2 to 61)
#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
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

Mpz_get_str(gmp_str, 10, x1)

If Len(*gmp_str) = n Then
ReDim d(10)

For i = 0 To n-1
d(gmp_str[i] - Asc("0")) += 1
Next i

If n9 = d(9) AndAlso n8 = d(8) AndAlso n7 = d(7) AndAlso n6 = d(6)_
AndAlso n5 = d(5) AndAlso n4 = d(4) AndAlso n3 = d(3)_
AndAlso n2 = d(2) AndAlso n1 = d(1) AndAlso n0 = d(0) Then
Print *gmp_str
End If
ElseIf Len(*gmp_str) < n Then
' all for next loops have a negative step value
' if len(str_x) becomes smaller then n it's time to try the next n value
' GoTo label1   ' old school BASIC
' prefered FreeBASIC style
Exit   For, For, For, For, For, For, For, For, For
' leave n1,  n2,  n3,  n4,  n5,  n6,  n7,  n8,  n9 loop
' and continue's after next n9
End If

Next n1
Next n2
Next n3
Next n4
Next n5
Next n6
Next n7
Next n8
Next n9
' label1:
Next n

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

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

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

### GW-BASIC

Translation of: FreeBASIC

Maximum for N (double) is14 digits, there are no 15 digits numbers

```1 DEFINT A-W : DEFDBL X-Z : DIM D(9) : DIM X2(9) : KEY OFF : CLS
2 FOR A = 0 TO 9 : X2(A) = A : NEXT A
3 FOR N = 1 TO 7
4 FOR N9 = N TO 0 STEP -1
5 FOR N8 = N-N9 TO 0 STEP -1
6 FOR N7 = N-N9-N8 TO 0 STEP -1
7 FOR N6 = N-N9-N8-N7 TO 0 STEP -1
8 FOR N5 = N-N9-N8-N7-N6 TO 0 STEP -1
9 FOR N4 = N-N9-N8-N7-N6-N5 TO 0 STEP -1
10 FOR N3 = N-N9-N8-N7-N6-N5-N4 TO 0 STEP -1
11 FOR N2 = N-N9-N8-N7-N6-N5-N4-N3 TO 0 STEP -1
12 FOR N1 = N-N9-N8-N7-N6-N5-N4-N3-N2 TO 0 STEP -1
13 N0 = N-N9-N8-N7-N6-N5-N4-N3-N2-N1
14 X = N1 + N2*X2(2) + N3*X2(3) + N4*X2(4) + N5*X2(5) + N6*X2(6) + N7*X2(7) + N8*X2(8) + N9*X2(9)
15 S\$ = MID\$(STR\$(X),2)
16 IF LEN(S\$) < N THEN GOTO 25
17 IF LEN(S\$) <> N THEN GOTO 24
18 FOR A = 0 TO 9 : D(A) = 0 : NEXT A
19 FOR A = 0 TO N-1
20 B = ASC(MID\$(S\$,A+1,1))-48
21 D(B) = D(B) + 1
22 NEXT A
23 IF N0 = D(0) AND N1 = D(1) AND N2 = D(2) AND N3 = D(3) AND N4 = D(4) AND N5 = D(5) AND N6 = D(6) AND N7 = D(7) AND N8 = D(8) AND N9 = D(9) THEN PRINT X,
24 NEXT N1 : NEXT N2 : NEXT N3 : NEXT N4 : NEXT N5 : NEXT N6 : NEXT N7 : NEXT N8 : NEXT N9
25 FOR A = 2 TO 9
26 X2(A) = X2(A) * A
27 NEXT A
28 NEXT N
29 PRINT
30 PRINT "done"
31 END
```
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```

### VBA

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

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

### VBScript

```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)
```
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,`

### ZX Spectrum Basic

Array index starts at 1. Only 1 character long variable names are allowed for For-Next loops. 8 Digits or higher numbers are displayed as floating point numbers. Needs about 2 hours (3.5Mhz)

``` 1 DIM K(10): DIM M(10)
2 FOR Y=0 TO 9: LET M(Y+1)=Y: NEXT Y
3 FOR N=1 TO 7
4 FOR J=N TO 0 STEP -1
5 FOR I=N-J TO 0 STEP -1
6 FOR H=N-J-I TO 0 STEP -1
7 FOR G=N-J-I-H TO 0 STEP -1
8 FOR F=N-J-I-H-G TO 0 STEP -1
9 FOR E=N-J-I-H-G-F TO 0 STEP -1
10 FOR D=N-J-I-H-G-F-E TO 0 STEP -1
11 FOR C=N-J-I-H-G-F-E-D TO 0 STEP -1
12 FOR B=N-J-I-H-G-F-E-D-C TO 0 STEP -1
13 LET A=N-J-I-H-G-F-E-D-C-B
14 LET X=B+C*M(3)+D*M(4)+E*M(5)+F*M(6)+G*M(7)+H*M(8)+I*M(9)+J*M(10)
15 LET S\$=STR\$ (X)
16 IF LEN (S\$)<N THEN GO TO 34
17 IF LEN (S\$)<>N THEN GO TO 33
18 FOR Y=1 TO 10: LET K(Y)=0: NEXT Y
19 FOR Y=1 TO N
20 LET Z= CODE (S\$(Y))-47
21 LET K(Z)=K(Z)+1
22 NEXT Y
23 IF A<>K(1) THEN GO TO 33
24 IF B<>K(2) THEN GO TO 33
25 IF C<>K(3) THEN GO TO 33
26 IF D<>K(4) THEN GO TO 33
27 IF E<>K(5) THEN GO TO 33
28 IF F<>K(6) THEN GO TO 33
29 IF G<>K(7) THEN GO TO 33
30 IF H<>K(8) THEN GO TO 33
31 IF I<>K(9) THEN GO TO 33
32 IF J=K(10) THEN PRINT X,
33 NEXT B: NEXT C: NEXT D: NEXT E: NEXT F: NEXT G: NEXT H: NEXT I: NEXT J
34 FOR Y=2 TO 9
35 LET M(Y+1)=M(Y+1)*Y
36 NEXT Y
37 NEXT N
38 PRINT
39 PRINT "DONE"
```
Output:
```9               8
7               6
5               4
3               2
1               0
9               8
7               6
5               4
3               2
1               0
407             371
370             153
9474            8208
1634            93084
92727           54748
548834          9926315
9800817         4210818
1741725```

## Befunge

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

```p55*\>:>:>:55+%\55+/00gvv_@
>1>+>^v\_^#!:<p01p00:+1<>\>
>#-_>\>20p110g>\20g*\v>1-v|
^!p00:-1g00+\$_^#!:<-1<^\.:<
```
Output:
`0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315`

## BQN

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

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

/IsNarc¨ ↕1e7```
`⟨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⟩`

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

`/ ↕∘≠⊸= ∾ (⥊0+⌜´(0=↕)↓¨(<↕10)⋆⊢)¨↕8`

## C

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

The following prints the first 25 numbers, though not in order...

```#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 {
++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;
}
```
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#

```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...");
}
}
}
```
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

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

### All 89 terms

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

static class Program
{
public static void nar(int max, bool only1 = false)
{
int n, n1, n2, n3, n4, n5, n6, n7, n8, n9;
int[] d;                                       // digits tally
char [] bs;                                    // BigInteger String
List<BigInteger> res = new List<BigInteger>(); // per n digits results
BigInteger[,] p = new BigInteger[10, max + 1]; // powers array

// BigIntegers for intermediate results
BigInteger x2, x3, x4, x5, x6, x7, x8, x9;

for (n = only1 ? max : 1; n <= max; n++) // main loop
{
for (int i = 1; i <= 9; i++) // init powers array for this n
{
p[i, 1] = BigInteger.Pow(i, n);
for (int j = 2; j <= n; j++) p[i, j] = p[i, 1] * j;
}
for (n9 = n; n9 >= 0; n9--) // nested loops...
{
x9 = p[9, n9];
for (n8 = n - n9; n8 >= 0; n8--)
{
x8 = x9 + p[8, n8];
for (n7 = n - n9 - n8; n7 >= 0; n7--)
{
x7 = x8 + p[7, n7];
for (n6 = n - n9 - n8 - n7; n6 >= 0; n6--)
{
x6 = x7 + p[6, n6];
for (n5 = n - n9 - n8 - n7 - n6; n5 >= 0; n5--)
{
x5 = x6 + p[5, n5];
for (n4 = n - n9 - n8 - n7 - n6 - n5; n4 >= 0; n4--)
{
x4 = x5 + p[4, n4];
for (n3 = n - n9 - n8 - n7 - n6 - n5 - n4; n3 >= 0; n3--)
{
x3 = x4 + p[3, n3];
for (n2 = n - n9 - n8 - n7 - n6 - n5 - n4 - n3; n2 >= 0; n2--)
{
x2 = x3 + p[2, n2];
for (n1 = n - n9 - n8 - n7 - n6 - n5 - n4 - n3 - n2; n1 >= 0; n1--)
{
bs = (x2 + n1).ToString().ToCharArray();
switch (bs.Length.CompareTo(n))
{ // Since all the for/next loops step down, when the digit count
// becomes smaller than n, it's time to try the next n value.
case -1: { goto Next_n; }
case 0:
{
d = new int[10]; foreach (char c in bs) d[c - 48] += 1;
if (n9 == d[9] && n8 == d[8] && n7 == d[7] &&
n6 == d[6] && n5 == d[5] && n4 == d[4] &&
n3 == d[3] && n2 == d[2] && n1 == d[1] &&
n - n9 - n8 - n7 - n6 - n5 - n4 - n3 - n2 - n1 == d[0])
break;
}
}
}
}
}
}
}
}
}
}
}
Next_n:     if (only1) {
Console.Write("{0} ", n); lock (resu) resu.AddRange(res); return;
} else {
res.Sort(); Console.WriteLine("{2,3} {0,3}: {1}",
Math.Ceiling((DateTime.Now - st).TotalSeconds), string.Join(" ", res), n); res.Clear();
}
}
}

private static DateTime st = default(DateTime);
private static List<BigInteger> resu = new List<BigInteger>();
private static bool para = true; // parallel (default) or sequential calcualtion
private static int lim = 7;  // this is the number of digits to calcualate, not the nth entry.
// for up to the 25th item, use lim = 7 digits.
// for all 89 items, use lim = 39 digits.
public static void Main(string[] args)
{
if (args.Count() > 0)
{
int t = lim; int.TryParse(args[0], out t);
if (t < 1) t = 1;   // number of digits must be > 0
if (t > 61) t = 61; // no point when lim * math.pow(9, lim) < math.pow(10, lim - 1)
lim = t;
// default is parallel, will do sequential when any 2nd command line parameter is present.
para = !(args.Count() > 1);
}
st = DateTime.Now;
if (para)
{
Console.Write("Calculations in parallel... "); // starts the bigger ones first
Parallel.ForEach(Enumerable.Range(1, lim).Reverse().ToArray(), n => { nar(n, true); } );
resu.Sort(); int[] g = Enumerable.Range(1, resu.Count).ToArray();
var both = g.Zip(resu, (a, b) => a.ToString() + " " + b.ToString());
Console.WriteLine("\n{0}", string.Join("\n", both));
}
else { Console.WriteLine("Sequential calculations:"); nar(lim); }
Console.WriteLine("Total elasped: {0} seconds", (DateTime.Now - st).TotalSeconds);
}
}
```
Output:
(with command line parameter = "39")
```Calculations in parallel... 7 6 5 4 3 2 1 11 10 9 8 15 14 13 12 19 18 17 16 23 22 20 21 26 27 25 24 30 31 29 34 28 35 38 33 39 32 37 36
1 0
2 1
3 2
4 3
5 4
6 5
7 6
8 7
9 8
10 9
11 153
12 370
13 371
14 407
15 1634
16 8208
17 9474
18 54748
19 92727
20 93084
21 548834
22 1741725
23 4210818
24 9800817
25 9926315
26 24678050
27 24678051
28 88593477
29 146511208
30 472335975
31 534494836
32 912985153
33 4679307774
34 32164049650
35 32164049651
36 40028394225
37 42678290603
38 44708635679
39 49388550606
40 82693916578
41 94204591914
42 28116440335967
43 4338281769391370
44 4338281769391371
45 21897142587612075
46 35641594208964132
47 35875699062250035
48 1517841543307505039
49 3289582984443187032
50 4498128791164624869
51 4929273885928088826
52 63105425988599693916
53 128468643043731391252
54 449177399146038697307
55 21887696841122916288858
56 27879694893054074471405
57 27907865009977052567814
58 28361281321319229463398
59 35452590104031691935943
60 174088005938065293023722
61 188451485447897896036875
62 239313664430041569350093
63 1550475334214501539088894
64 1553242162893771850669378
65 3706907995955475988644380
66 3706907995955475988644381
67 4422095118095899619457938
68 121204998563613372405438066
69 121270696006801314328439376
70 128851796696487777842012787
71 174650464499531377631639254
72 177265453171792792366489765
73 14607640612971980372614873089
74 19008174136254279995012734740
75 19008174136254279995012734741
76 23866716435523975980390369295
77 1145037275765491025924292050346
78 1927890457142960697580636236639
79 2309092682616190307509695338915
80 17333509997782249308725103962772
81 186709961001538790100634132976990
82 186709961001538790100634132976991
83 1122763285329372541592822900204593
84 12639369517103790328947807201478392
85 12679937780272278566303885594196922
86 1219167219625434121569735803609966019
87 12815792078366059955099770545296129367
88 115132219018763992565095597973971522400
89 115132219018763992565095597973971522401
Total elasped: 443.8791684 seconds```

(without any command line parameters)

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

(with command line parameters= "7 x")

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

(with command line parameters= "25 x")

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

## C++

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

## Clojure

Find N first Narcissistic numbers.

```(ns narcissistic.core
(:require [clojure.math.numeric-tower :as math]))

(defn digits [n] ;; digits of a number.
(->> n str (map (comp read-string str))))

(defn narcissistic? [n] ;; True if the number is a Narcissistic one.
(let [d (digits n)
s (count d)]
(= n (reduce + (map #(math/expt % s) d)))))

(defn firstNnarc [n] ;;list of the first "n" Narcissistic numbers.
(take n (filter narcissistic? (range))))
```
Output:

by Average-user

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

## COBOL

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

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

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

MOVE 20 TO counter.
PERFORM UNTIL counter=0

PERFORM 000-NARCISSIST-PARA

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

END-PERFORM

STOP RUN.

000-NARCISSIST-PARA.

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

PERFORM  UNTIL temp=0

DIVIDE temp BY 10 GIVING temp
REMAINDER  modulo

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

END-PERFORM.

IF current-number=in-sum
END-IF.

END PROGRAM NARCISSIST-NUMS.
```
Output:
```the first 20 narcissist numbers:
0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084

```

## Common Lisp

```(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))))
```
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

```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));
}
```
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
```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));
}
```

With LDC2 compiler prints the same output in less than 0.3 seconds.

### Faster Version

Translation of: C
```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);
}
```
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
```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
```
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

```PROGRAM NARCISISTIC

!\$DOUBLE

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

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#

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

## Factor

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

: digit-count ( n -- count ) log10 floor >integer 1 + ;

: narcissist? ( n -- ? ) dup [ 1 digit-groups ]
[ digit-count [ ^ ] curry ] bi map-sum = ;

: first25 ( -- seq ) 25 0 lfrom [ narcissist? ] lfilter
ltake list>array ;

: main ( -- ) first25 [ pprint bl ] each ;

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

## Forth

Works with: GNU Forth version 0.7.0
``` : dig.num                           \ returns input number and the number of its digits ( n -- n n1 )
dup
0 swap
begin
swap 1 + swap
dup 10 >= while
10 /
repeat
drop ;

: zero.divmod                         \ /mod that returns zero if number is zero
dup
0 = if drop 0 else
/mod
then ;

: zero.div                            \ division that returns zero if divisor is zero
dup
0 = if drop else
/
then ;

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

: ten.to			          \ ( n -- 10^n ) returns 1 for zero and negative
dup 0 <= if drop 1 else
dup 1 = if drop 10 else
10 swap
1 do
10 *
loop then then ;

: split.div                                        \ returns input number and its digits ( n -- n n1 n2 n3....)
dup 10 < if dup  else		    \ duplicates single digit numbers
dig.num				    \ provides number of digits
swap dup rot dup 1 - ten.to swap         \ stack juggling, ten raised to number of digits - 1...
1 do                                     \ ... is the needed divisor, counter on top and ...
dup rot swap zero.divmod swap rot 10 /   \ ...division loop
loop drop then ;

: to.pow                           \ nth power of positive numbers ( n m -- n^m )
swap dup rot
dup 0 <= if
2drop drop 1
else
0 do
swap dup rot *
loop
swap zero.div
then ;

: num.pow                        \ raises each digit to the power of (number of digits)
depth 1 - 0 do
next.last depth 1 - to.pow
loop ;

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

: narc.check
split.div
num.pow

: narc.num 0 { a b }              \  ( m -- n1 n2 n3 ... nm )
page                      \ displays m narcissistic decimal numbers...
999999999 0 do            \ ...beginning with 0
a b = if leave then
i narc.check = if
i . cr b 1 + to b
then
loop
;

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

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

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

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

## Go

Nothing fancy as it runs in a fraction of a second as-is.

```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))
}
```
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]
```

### Exhaustive search (integer series)

```import Data.Char (digitToInt)

isNarcissistic :: Int -> Bool
isNarcissistic n = (sum ((^ digitCount) <\$> digits) ==) n
where
digits = digitToInt <\$> show n
digitCount = length digits

main :: IO ()
main = mapM_ print \$ take 25 (filter isNarcissistic [0 ..])
```

### Reduced search (unordered digit combinations)

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

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

```import Data.Bifunctor (second)

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

isDaffodil :: Int -> Int -> Bool
isDaffodil e n =
(((&&) . (e ==) . length) <*> (n ==) . powerSum e) (digitList n)

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

digitList :: Int -> [Int]
digitList 0 = [0]
digitList n = go n
where
go 0 = []
go x = rem x 10 : go (quot x 10)

--------------------------- TEST ---------------------------
main :: IO ()
main =
putStrLn \$
fTable
"Narcissistic decimal numbers of length 1-7:\n"
show
show
narcissiOfLength
[1 .. 7]

fTable :: String -> (a -> String) -> (b -> String) -> (a -> b) -> [a] -> String
fTable s xShow fxShow f xs =
let rjust n c = drop . length <*> (replicate n c ++)
w = maximum (length . xShow <\$> xs)
in unlines \$
s : fmap (((++) . rjust w ' ' . xShow) <*> ((" -> " ++) . fxShow . f)) xs
```
Output:
```Narcissistic decimal numbers of length 1-7:

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

## Icon and Unicon

The following is a quick, dirty, and slow solution that works in both languages:

```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
```

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

```getDigits=: "."0@":                  NB. get digits from number
isNarc=: (= +/@(] ^ #)@getDigits)"0  NB. test numbers for Narcissism
```

Example Usage

```   (#~ 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
```

## Java

Works with: Java version 1.5+
```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++;
}
}
}
}
```
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!

```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();

for (int count = 0; count < length; count++) {
int value = Integer.parseInt(String.valueOf(i.toString().charAt(count)));
}

numbersCalculated++;
}

if (numbersCalculated == numbersToCalculate) {
System.exit(0);
}
});
}
}
```
Output:
`0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 `

## JavaScript

### ES5

Translation of: Java
```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(' ');
}
```
Output:
`"0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315"`

### ES6

#### Exhaustive search (integer series)

```(() => {
'use strict';

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

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

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

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

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

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

#### Reduced search (unordered digit combinations)

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

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

(Generating the unordered digit combinations directly as power sums allows faster testing later, and needs less space)

```(() => {
'use strict';

// main :: IO ()
const main = () =>
console.log(
fTable(
'Narcissistic decimal numbers of lengths [1..7]:\n'
)(show)(show)(
narcissiOfLength
)(enumFromTo(1)(7))
);

// narcissiOfLength :: Int -> [Int]
const narcissiOfLength = n =>
0 < n ? filter(isDaffodil(n))(
digitPowerSums(n)
) : [0];

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

// isDaffodil :: Int -> Int -> Bool
const isDaffodil = e => n => {
// True if the decimal digits of N,
// each raised to the power E, sum to N.
const ds = digitList(n);
return e === ds.length && n === powerSum(e)(ds);
};

// The subset of integers of n digits that actually need daffodil checking:

// (Flattened leaves of a tree of unique digit combinations, in which
// order is not significant. Digit sequence doesn't affect power summing)

// digitPowerSums :: Int -> [Int]
const digitPowerSums = nDigits => {
const
digitPowers = map(x => [x, pow(x, nDigits)])(
enumFromTo(0)(9)
),
treeGrowth = (n, parentPairs) => 0 < n ? (
treeGrowth(n - 1,
isNull(parentPairs) ? (
digitPowers
) : concatMap(
([parentDigit, parentSum]) =>
map(([leafDigit, leafSum]) => //
[leafDigit, parentSum + leafSum])(
take(parentDigit + 1)(digitPowers)
)
)(parentPairs)
)
) : parentPairs;
return map(snd)(treeGrowth(nDigits, []));
};

// ---------------------GENERIC FUNCTIONS---------------------

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m => n =>
Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// concatMap :: (a -> [b]) -> [a] -> [b]
const concatMap = f =>
xs => xs.flatMap(f);

// cons :: a -> [a] -> [a]
const cons = x =>
xs => [x].concat(xs);

// digitList :: Int -> [Int]
const digitList = n => {
const go = x => 0 < x ? (
cons(x % 10)(
go(Math.floor(x / 10))
)
) : [];
return 0 < n ? go(n) : [0];
}

// filter :: (a -> Bool) -> [a] -> [a]
const filter = f => xs => xs.filter(f);

// map :: (a -> b) -> [a] -> [b]
const map = f =>
xs => xs.map(f);

// isNull :: [a] -> Bool
// isNull :: String -> Bool
const isNull = xs =>
1 > xs.length;

// length :: [a] -> Int
const length = xs => xs.length;

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

// take :: Int -> [a] -> [a]
const take = n =>
xs => xs.slice(0, n);

// snd :: (a, b) -> b
const snd = tpl => tpl[1];

// show :: a -> String
const show = x => JSON.stringify(x)

// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
const zipWith = f => xs => ys =>
xs.slice(
0, Math.min(xs.length, ys.length)
).map((x, i) => f(x)(ys[i]));

// ------------------------FORMATTING-------------------------

// fTable :: String -> (a -> String) -> (b -> String)
//                      -> (a -> b) -> [a] -> String
const fTable = s => xShow => fxShow => f => xs => {
// Heading -> x display function ->
//           fx display function ->
//    f -> values -> tabular string
const
ys = xs.map(xShow),
w = Math.max(...ys.map(length));
return s + '\n' + zipWith(
a => b => a.padStart(w, ' ') + ' -> ' + b
)(ys)(
xs.map(x => fxShow(f(x)))
).join('\n');
};

// MAIN ---
return main();
})();
```
Output:
```Narcissistic decimal numbers of lengths [1..7]:

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

## jq

Works with: jq version 1.4

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

```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;```

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:

```# Input:  [i, [0^i, 1^i, 2^i, ..., 9^i]]
# Output: [j, [0^j, 1^j, 2^j, ..., 9^j]]
# 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;```

The function is_narcisstic can now be modified to use powers(j) as follows:

```# 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;```

```# 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;

# 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)```
Output:
```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
```

## Julia

This easy to implement brute force technique is plenty fast enough to find the first few Narcissistic decimal numbers.

```using Printf  # for Julia version 1.0+

function isnarcissist(n, b=10)
-1 < n || return false
d = digits(n, base=b)
m = length(d)
n == mapreduce((x)->x^m, +, d)
end

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

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

## Kotlin

```// version 1.1.0

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

fun main(args: Array<String>) {
println("The first 25 narcissistic (or Armstrong) numbers are:")
var i = 0
var count = 0
do {
if (isNarcissistic(i)) {
print("\$i ")
count++
}
i++
}
while (count < 25)
}
```
Output:
```The first 25 narcissistic (or Armstrong) numbers are:
0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315
```

## Ksh

```#!/bin/ksh

# Narcissistic decimal number

#	# Variables:
#

#	# Functions:
#

#	# Function _isnarcissist(n) - return 1 if n is a narcissistic decimal number
#
function _isnarcissist {
typeset _n ; integer _n=\$1

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

#	# Function _sumpowdigits(n) - return sum of the digits raised to #digit power
#
function _sumpowdigits {
typeset _n ; integer _n=\$1
typeset _i ; typeset -si _i
typeset _sum ; integer _sum=0

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

######
# main #
######

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

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

## Maple

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

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

## Mathematica/Wolfram Language

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

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

## Nanoquery

```def is_narcissist(num)
digits = {}
for digit in str(num)
digits.append(int(digit))
end

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

return sum = num
end

def narcissist(n)
results = {}

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

return results
end

// get 25 narcissist numbers
for num in narcissist(25)
print num + " "
end
println```
Output:
`0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 `

## Nim

A simple solution which runs in about one second.

```import sequtils, strutils

func digits(n: Natural): seq[int] =
var n = n div 10
while n != 0:
n = n div 10

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

echo findNarcissistic(25).join(" ")
```
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`

## OCaml

Exhaustive search (integer series)
```let narcissistic =
let rec next n l p () =
let rec digit_pow_sum a n =
if n < 10 then a + p.(n) else digit_pow_sum (a + p.(n mod 10)) (n / 10)
in
if n = l then next n (l * 10) (Array.mapi ( * ) p) ()
else if n = digit_pow_sum 0 n then Seq.Cons (n, next (succ n) l p)
else next (succ n) l p ()
in
next 0 10 (Array.init 10 Fun.id)

let () =
narcissistic |> Seq.take 25 |> Seq.iter (Printf.printf " %u") |> print_newline
```
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

```: 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 ;```
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.

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

## Pascal

### Free Pascal

A recursive version starting at the highest digit and recurses to digit 0. Bad runtime. One more digit-> 10x runtime runtime ~ 10^(count of Digits).

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

real	0m1.000s```

#### alternative

recursive solution.Just counting the different combination of digits
See Combinations_with_repetitions

```program PowerOwnDigits;
{\$IFDEF FPC}
{\$MODE DELPHI}{\$OPTIMIZATION ON,ALL}{\$COPERATORS ON}
{\$ELSE}{\$APPTYPE CONSOLE}{\$ENDIF}
uses
SysUtils;

const
MAXBASE = 10;
MaxDgtVal = MAXBASE - 1;
MaxDgtCount = 19;
type
tDgtCnt = 0..MaxDgtCount;
tValues = 0..MaxDgtVal;
tUsedDigits = array[0..23] of Int8;
tpUsedDigits = ^tUsedDigits;
tPower = array[tValues] of Uint64;
var
PowerDgt: array[tDgtCnt] of tPower;
Min10Pot : array[tDgtCnt] of Uint64;
gblUD  : tUsedDigits;
CombIdx: array of Int8;
Numbers : array of Uint64;
rec_cnt : NativeInt;

procedure OutUD(const UD:tUsedDigits);
var
i : integer;
begin
For i in tValues do
write(UD[i]:3);
writeln;
For i := 0 to MaxDgtCount do
write(CombIdx[i]:3);
writeln;
end;

function InitCombIdx(ElemCount: Byte): pbyte;
begin
setlength(CombIdx, ElemCount + 1);
Fillchar(CombIdx[0], sizeOf(CombIdx[0]) * (ElemCount + 1), #0);
Result := @CombIdx[0];
Fillchar(gblUD[0], sizeOf(gblUD[0]) * (ElemCount + 1), #0);
gblUD[0]:= 1;
end;

function Init(ElemCount:byte):pByte;
var
pP1,Pp2 : pUint64;
i, j: Int32;
begin
Min10Pot[0]:= 0;
Min10Pot[1]:= 1;
for i := 2 to High(tDgtCnt) do
Min10Pot[i]:=Min10Pot[i-1]*MAXBASE;

pP1 := @PowerDgt[low(tDgtCnt)];
for i in tValues do
pP1[i] := 1;
pP1[0] := 0;
for j := low(tDgtCnt) + 1 to High(tDgtCnt) do
Begin
pP2 := @PowerDgt[j];
for i in tValues do
pP2[i] := pP1[i]*i;
pP1 := pP2;
end;
result := InitCombIdx(ElemCount);
gblUD[0]:= 1;
end;

function GetPowerSum(minpot:nativeInt;digits:pbyte;var UD :tUsedDigits):NativeInt;
var
pPower : pUint64;
res,r  : Uint64;
dgt :Int32;
begin
r := Min10Pot[minpot];
dgt := minpot;
res := 0;
pPower := @PowerDgt[minpot,0];
repeat
dgt -=1;
res += pPower[digits[dgt]];
until dgt=0;
//check if res within bounds of digitCnt
result := 0;
if (res<r) or (res>r*MAXBASE) then  EXIT;

//convert res into digits
repeat
r := res DIV MAXBASE;
result+=1;
UD[res-r*MAXBASE]-= 1;
res := r;
until r = 0;
end;

procedure calcNum(minPot:Int32;digits:pbyte);
var
UD :tUsedDigits;
res: Uint64;
i: nativeInt;
begin
UD := gblUD;
If GetPowerSum(minpot,digits,UD) <>0 then
Begin
//don't check 0
i := 1;
repeat
If UD[i] <> 0 then
Break;
i +=1;
until i > MaxDgtVal;

if i > MaxDgtVal then
begin
res := 0;
for i := minpot-1 downto 0 do
res += PowerDgt[minpot,digits[i]];
setlength(Numbers, Length(Numbers) + 1);
Numbers[high(Numbers)] := res;
end;
end;
end;

function NextCombWithRep(pComb: pByte;pUD :tpUsedDigits;MaxVal, ElemCount: UInt32): boolean;
var
i,dgt: NativeInt;
begin
i := -1;
repeat
i += 1;
dgt := pComb[i];
if dgt < MaxVal then
break;
dec(pUD^[dgt]);
until i >= ElemCount;
Result := i >= ElemCount;

if i = 0 then
begin
dec(pUD^[dgt]);
dgt +=1;
pComb[i] := dgt;
inc(pUD^[dgt]);
end
else
begin
//decrements digit 0 too.This is false, but not checked.
dec(pUD^[dgt]);
dgt +=1;
pUD^[dgt]:=i+1;
repeat
pComb[i] := dgt;
i -= 1;
until i < 0;
end;
end;

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

begin
digits := Init(MaxDgtCount);
T0 := GetTickCount64;
rec_cnt := 0;
// i > 0
For i := 2 to MaxDgtCount do
Begin
digits := InitCombIdx(MaxDgtCount);
repeat
calcnum(i,digits);
inc(rec_cnt);
until NextCombWithRep(digits,@gblUD,MaxDgtVal,i);
writeln(i:3,' digits with ',Length(Numbers):3,' solutions in ',GetTickCount64-T0:5,' ms');
end;
T0 := GetTickCount64-T0;
writeln(rec_cnt,' recursions');

//sort
for i := 0 to High(Numbers) - 1 do
for j := i + 1 to High(Numbers) do
if Numbers[j] < Numbers[i] then
begin
tmp := Numbers[i];
Numbers[i] := Numbers[j];
Numbers[j] := tmp;
end;

setlength(Numbers, j + 1);
for i := 0 to High(Numbers) do
writeln(i+1:3,Numbers[i]:20);
setlength(Numbers, 0);
setlength(CombIdx,0);
{\$IFDEF WINDOWS}
{\$ENDIF}
end.
```
@TIO.RUN:
```  2 digits with   0 solutions in     0 ms
3 digits with   4 solutions in     0 ms
4 digits with   7 solutions in     0 ms
5 digits with  10 solutions in     0 ms
6 digits with  11 solutions in     0 ms
7 digits with  15 solutions in     0 ms
8 digits with  18 solutions in     1 ms
9 digits with  22 solutions in     3 ms
10 digits with  23 solutions in     6 ms
11 digits with  31 solutions in    13 ms
12 digits with  31 solutions in    25 ms
13 digits with  31 solutions in    46 ms
14 digits with  32 solutions in    82 ms
15 digits with  32 solutions in   141 ms
16 digits with  34 solutions in   238 ms
17 digits with  37 solutions in   395 ms
18 digits with  37 solutions in   644 ms
19 digits with  41 solutions in  1028 ms
20029999 recursions
1                 153
2                 370
3                 371
4                 407
5                1634
6                8208
7                9474
8               54748
9               92727
10               93084
11              548834
12             1741725
13             4210818
14             9800817
15             9926315
16            24678050
17            24678051
18            88593477
19           146511208
20           472335975
21           534494836
22           912985153
23          4679307774
24         32164049650
25         32164049651
26         40028394225
27         42678290603
28         44708635679
29         49388550606
30         82693916578
31         94204591914
32      28116440335967
33    4338281769391370
34    4338281769391371
35   21897142587612075
36   35641594208964132
37   35875699062250035
38 1517841543307505039
39 3289582984443187032
40 4498128791164624869
41 4929273885928088826```

## Perl

Simple version using a naive predicate.

```use v5.36;

sub is_narcissistic (\$n) {
my(\$k, \$sum) = (length \$n, 0);
\$sum += \$_**\$k for split '', \$n;
\$n == \$sum
}

my (\$i,@N) = 0;
while (@N < 25) {
\$i++ while not is_narcissistic \$i;
push @N, \$i++
}

say join ' ', @N;
```
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`

## Phix

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

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

### faster

Translation of: AppleScript

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

```with javascript_semantics
-- Begin with zero, which is narcissistic by definition and is never the only digit used in other numbers.
sequence output = {`0`}
bool done = false
integer m = 0
integer q
atom t0 = time()

procedure recurse(string digits, atom powsum, integer rem)
-- Recursive subhandler. Builds lists containing m digit values while summing the digits' mth powers.
-- If m digits have been obtained, compare the sum of powers's digits with the values in the list.
-- Otherwise continue branching the recursion to derive longer lists.
if rem=0 then
atom temp = powsum
integer unmatched = m
while temp do
integer d = find('0'+remainder(temp,10),digits)
if d=0 then exit end if
digits[d] = ' '
unmatched -= 1
temp = floor(temp/10)
end while
-- If all the digits have been matched, the sum of powers is narcissistic.
if unmatched=0 then
output = append(output,sprintf("%d",powsum))
if length(output)=q then done = true end if
end if
else
-- If fewer than m digits at this level, derive longer lists from the current one.
-- Adding only values that are less than or equal to the last one makes each
-- collection unique and turns up the narcissistic numbers in numerical order.
--
-- ie/eg if sum(sq_power({9,7,4,4},4))==9474, and as shown sort(digits)==list,
-- then 9474 is the one and only permutation that is narcissistic, obviously,
-- and there is no point looking at any other permutation of that list, ever.
-- Also 1000,1100,1110,1111 are the only 4 lists beginning 1, as opposed to
-- the 999 four-digit numbers beginning 1 that might otherwise be checked,
-- and likewise 9000..9999 is actually just 220 rather than the full 999.
-- (I can see that exploring smaller partial sums first will tend to issue
--  results in numeric order, but cannot see an absolute certainty of that)
--
for d=0 to digits[\$]-'0' do
recurse(digits & d+'0', powsum + power(d,m), rem-1)
if done then exit end if
end for
end if
end procedure

function narcissisticDecimalNumbers(integer qp)
atom t1 = time()+1
q = qp
-- Initiate the recursive building and testing of collections of increasing numbers of digit values.
while not done do
m += 1
if m > iff(machine_bits()=32?16:17) then
output = append(output,"Remaining numbers beyond number precision")
done = true
else
for digit=1 to 9 do
recurse(""&'0'+digit, power(digit,m), m-1)
if done then exit end if
end for
if not done and time()>t1 and platform()!=JS then
printf(1,"searching... %d found, length %d, %s\n",
{length(output),m,elapsed(time()-t0)})
t1 = time()+1
end if
end if
end while
return output
end function

sequence r = narcissisticDecimalNumbers(iff(machine_bits()=32?44:47))
pp(r)
printf(1,"found %d in %s\n",{length(r),elapsed(time()-t0)})
```
Output:
```searching... 41 found, length 13, 1.0s
searching... 42 found, length 15, 3.3s
searching... 44 found, length 16, 5.7s
{`0`, `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, `9`, `153`, `370`, `371`,
`407`, `1634`, `8208`, `9474`, `54748`, `92727`, `93084`, `548834`,
`1741725`, `4210818`, `9800817`, `9926315`, `24678050`, `24678051`,
`88593477`, `146511208`, `472335975`, `534494836`, `912985153`,
`4679307774`, `32164049650`, `32164049651`, `40028394225`, `42678290603`,
`44708635679`, `49388550606`, `82693916578`, `94204591914`,
`28116440335967`, `4338281769391370`, `4338281769391371`,
`21897142587612075`, `35641594208964132`, `35875699062250035`}
found 47 in 8.2s
```

## PicoLisp

```(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)```

## PL/I

### version 1

Translation of: REXX
``` narn: Proc Options(main);
Dcl (j,k,l,nn,n,sum) Dec Fixed(15)init(0);
Dcl s Char(15) Var;
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;```
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

```*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 (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;
```
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

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

## Python

### Procedural

This solution pre-computes the powers once.

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

### Functional

Translation of: JavaScript
Works with: Python version 3.7
```'''Narcissistic decimal numbers'''

from itertools import chain
from functools import reduce

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

# narcissiOfLength :: Int -> [Int]
def narcissiOfLength(n):
'''List of Narcissistic numbers of
(base 10) digit length n.
'''
return [
x for x in digitPowerSums(n)
if isDaffodil(n)(x)
]

# digitPowerSums :: Int -> [Int]
def digitPowerSums(e):
'''The subset of integers of e digits that are potential narcissi.
(Flattened leaves of a tree of unique digit combinations, in which
order is not significant. The sum is independent of the sequence.)
'''
powers = [(x, x ** e) for x in enumFromTo(0)(9)]

def go(n, parents):
return go(
n - 1,
chain.from_iterable(map(
lambda pDigitSum: (
map(
lambda lDigitSum: (
lDigitSum[0],
lDigitSum[1] + pDigitSum[1]
),
powers[0: 1 + pDigitSum[0]]
)
),
parents
)) if parents else powers
) if 0 < n else parents

return [xs for (_, xs) in go(e, [])]

# isDaffodil :: Int -> Int -> Bool
def isDaffodil(e):
'''True if n is a narcissistic number
of decimal digit length e.
'''
def go(n):
ds = digitList(n)
return e == len(ds) and n == powerSum(e)(ds)
return lambda n: go(n)

# powerSum :: Int -> [Int] -> Int
def powerSum(e):
'''The sum of a list obtained by raising
each element of xs to the power of e.
'''
return lambda xs: reduce(
lambda a, x: a + x ** e,
xs, 0
)

# -----------------------FORMATTING------------------------

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

# GENERIC -------------------------------------------------

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

# enumFromTo :: Int -> Int -> [Int]
def enumFromTo(m):
'''Enumeration of integer values [m..n]'''
def go(n):
return list(range(m, 1 + n))
return lambda n: go(n)

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```Narcissistic numbers of digit lengths 1 to 7:

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

## Quackery

```  [ [] swap
[ 10 /mod
rot join swap
dup 0 = until ]
drop ]                 is digits     ( n --> [   )

[ dup digits
0 over size rot
witheach
[ over ** rot + swap ]
drop = ]                 is narcissistic ( n --> b )

[] 0
[ dup narcissistic if
[ tuck join swap ]
1+ over size 25 = until ]
drop echo```
Output:
`[ 0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634 8208 9474 54748 92727 93084 548834 1741725 4210818 9800817 9926315 ]`

## R

### For loop solution

This is a slow method and it needed above 5 minutes on a i3 machine.

```for (u in 1:10000000) {
j <- nchar(u)
set2 <- c()
for (i in 1:j) {
set2[i] <- as.numeric(substr(u, i, i))
}
control <- c()
for (k in 1:j) {
control[k] <- set2[k]^(j)
}
if (sum(control) == u) print(u)
}
```
Output:
```[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
[1] 9
[1] 153
[1] 370
[1] 371
[1] 407
[1] 1634
[1] 8208
[1] 9474
[1] 54748
[1] 92727
[1] 93084
[1] 548834
[1] 1741725
[1] 4210818
[1] 9800817
[1] 9926315```

### While loop solution

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

• This solution allows us to control how many Armstrong numbers we generate.
• Rather than using a for loop that assumes that we will be done by the 10000000th case, we use a while loop.
• Rather than using nchar or as.character, which both misbehave if the inputs are large enough for R to default to scientific notation, we use format.
• We exploit many of R's vectorized functions, letting us avoid using any for loops.
• As we are using format anyway, we take the chance to make the output look nicer.
```generateArmstrong <- function(howMany)
{
resultCount <- i <- 0
while(resultCount < howMany)
{
#The next line looks terrible, but I know of no better way to convert a large integer in to its digits in R.
digits <- as.integer(unlist(strsplit(format(i, scientific = FALSE), "")))
if(i == sum(digits^(length(digits)))) cat("Armstrong number ", resultCount <- resultCount + 1, ": ", format(i, big.mark = ","), "\n", sep = "")
i <- i + 1
}
}
generateArmstrong(25)
```
Output:
```Armstrong number 1: 0
Armstrong number 2: 1
Armstrong number 3: 2
Armstrong number 4: 3
Armstrong number 5: 4
Armstrong number 6: 5
Armstrong number 7: 6
Armstrong number 8: 7
Armstrong number 9: 8
Armstrong number 10: 9
Armstrong number 11: 153
Armstrong number 12: 370
Armstrong number 13: 371
Armstrong number 14: 407
Armstrong number 15: 1,634
Armstrong number 16: 8,208
Armstrong number 17: 9,474
Armstrong number 18: 54,748
Armstrong number 19: 92,727
Armstrong number 20: 93,084
Armstrong number 21: 548,834
Armstrong number 22: 1,741,725
Armstrong number 23: 4,210,818
Armstrong number 24: 9,800,817
Armstrong number 25: 9,926,315```

## Racket

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

## Raku

(formerly Perl 6)

### Simple, with concurrency

Simple implementation is not exactly speedy, but concurrency helps move things along.

```sub is-narcissistic(Int \$n) { \$n == [+] \$n.comb »**» \$n.chars }
my @N = lazy (0..∞).hyper.grep: *.&is-narcissistic;
@N[^25].join(' ').say;
```
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`

This version that precalculates the values for base 1000 digits, but despite the extra work ends up taking more wall-clock time than the simpler version.

```sub kigits(\$n) {
my int \$i = \$n;
my int \$b = 1000;
gather while \$i {
take \$i % \$b;
\$i = \$i div \$b;
}
}

for (1..*) -> \$d {
my @t = 0..9 X** \$d;
my @table = @t X+ @t X+ @t;
sub is-narcissistic(\n) { n == [+] @table[kigits(n)] };
state \$l = 2;
FIRST say "1\t0";
say \$l++, "\t", \$_ if .&is-narcissistic for 10**(\$d-1) ..^ 10**\$d;
last if \$l > 25
};
```
Output:
```1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	153
12	370
13	371
14	407
15	1634
16	8208
17	9474
18	54748
19	92727
20	93084
21	548834
22	1741725
23	4210818
24	9800817
25	9926315```

## REXX

### idiomatic

```/*REXX program  generates and displays  a number of  narcissistic (Armstrong)  numbers. */
numeric digits 39                                /*be able to handle largest Armstrong #*/
parse arg N .                                    /*obtain optional argument from the CL.*/
if N=='' | N==","  then N=25                     /*Not specified?  Then use the default.*/
N=min(N, 89)                                     /*there are only  89  narcissistic #s. */
#=0                                              /*number of narcissistic numbers so far*/
do j=0  until #==N;     L=length(j)         /*get length of the  J  decimal number.*/
\$=left(j, 1) **L                            /*1st digit in  J  raised to the L pow.*/

do k=2  for L-1  until \$>j        /*perform for each decimal digit in  J.*/
\$=\$ + substr(j, k, 1) ** L        /*add digit raised to power to the sum.*/
end   /*k*/                       /* [↑]  calculate the rest of the sum. */

if \$\==j  then iterate                      /*does the sum equal to J?  No, skip it*/
#=# + 1                                     /*bump count of narcissistic numbers.  */
say right(#, 9)     ' narcissistic:'     j  /*display index and narcissistic number*/
end   /*j*/                                 /*stick a fork in it,  we're all done. */
```
output   when using the default input:
```        1  narcissistic: 0
2  narcissistic: 1
3  narcissistic: 2
4  narcissistic: 3
5  narcissistic: 4
6  narcissistic: 5
7  narcissistic: 6
8  narcissistic: 7
9  narcissistic: 8
10  narcissistic: 9
11  narcissistic: 153
12  narcissistic: 370
13  narcissistic: 371
14  narcissistic: 407
15  narcissistic: 1634
16  narcissistic: 8208
17  narcissistic: 9474
18  narcissistic: 54748
19  narcissistic: 92727
20  narcissistic: 93084
21  narcissistic: 548834
22  narcissistic: 1741725
23  narcissistic: 4210818
24  narcissistic: 9800817
25  narcissistic: 9926315
```

### optimized

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

It is about   77%   faster then 1st REXX version.

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

do     p=1  for 39                          /*generate tables:   digits ^ P power. */
do i=0  for 10;      @.p.i= i**p        /*build table of ten digits ^ P power. */
end   /*i*/
end       /*w*/                             /* [↑]  table is a fixed (limited) size*/
#=0                                              /*number of narcissistic numbers so far*/
do j=0  until #==N;      L=length(j)        /*get length of the  J  decimal number.*/
_=left(j, 1)                                /*select the first decimal digit to sum*/
\$=@.L._                                     /*sum of the J dec. digits ^ L (so far)*/
do k=2  for L-1  until \$>j        /*perform for each decimal digit in  J.*/
_=substr(j, k, 1)                 /*select the next decimal digit to sum.*/
\$=\$ + @.L._                       /*add dec. digit raised to power to sum*/
end   /*k*/                       /* [↑]  calculate the rest of the sum. */

if \$\==j  then iterate                      /*does the sum equal to J?  No, skip it*/
#=# + 1                                     /*bump count of narcissistic numbers.  */
say right(#, 9)     ' narcissistic:'     j  /*display index and narcissistic number*/
end   /*j*/                                 /*stick a fork in it,  we're all done. */
```
output   is identical to the 1st REXX version.

### optimized, unrolled

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

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

It is about     44%   faster then 2nd REXX version,   and
it is about   154%   faster then 1st REXX version.

```/*REXX program  generates and displays  a number of  narcissistic (Armstrong)  numbers. */
numeric digits 39                                /*be able to handle largest Armstrong #*/
parse arg N .                                    /*obtain optional argument from the CL.*/
if N=='' | N==","  then N=25                     /*Not specified?  Then use the default.*/
N=min(N, 89)                                     /*there are only  89  narcissistic #s. */
@.=0                                             /*set default for the @ stemmed array. */
#=0                                              /*number of narcissistic numbers so far*/
do p=0  for 39+1; if p<10  then call tell p /*display the 1st 1─digit dec. numbers.*/
do i=1  for 9;     @.p.i= i**p          /*build table of ten digits ^ P power. */
end   /*i*/
end       /*p*/                             /* [↑]  table is a fixed (limited) size*/
/* [↓]  skip the 2─digit dec. numbers. */
do j=100;              L=length(j)          /*get length of the  J  decimal number.*/
parse var  j    _1  2  _2  3  m  ''  -1  _R /*get 1st, 2nd, middle, last dec. digit*/
\$=@.L._1  +  @.L._2  +  @.L._R              /*sum of the J decimal digs^L (so far).*/

do k=3  for L-3  until \$>j         /*perform for other decimal digits in J*/
parse var  m    _  +1  m           /*get next dec. dig in J, start at 3rd.*/
\$=\$ + @.L._                        /*add dec. digit raised to pow to sum. */
end   /*k*/                        /* [↑]  calculate the rest of the sum. */

if \$==j  then do;  call tell j              /*does the sum equal to  J?  Show the #*/
if #==n  then leave      /*does the sum equal to  J?  Show the #*/
end
end   /*j*/                                 /* [↑]  the  J loop  list starts at 100*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
tell: #=# + 1                                    /*bump the counter for narcissistic #s.*/
say right(#,9)   ' narcissistic:'   arg(1) /*display index and narcissistic number*/
if #==n  &  n<11  then exit                /*finished showing of narcissistic #'s?*/
```
output   is identical to the 1st REXX version.

### optimized, 3-digit chunks

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

It is about     65%   faster then 3rd REXX version,   and
it is about   136%   faster then 2nd REXX version,   and
it is about   317%   faster then 1st REXX version.

```/*REXX program  generates and displays  a number of  narcissistic (Armstrong)  numbers. */
numeric digits 39                                /*be able to handle largest Armstrong #*/
parse arg N .                                    /*obtain optional argument from the CL.*/
if N=='' | N==","  then N=25                     /*Not specified?  Then use the default.*/
N=min(N, 89)                                     /*there are only  89  narcissistic #s. */
@.=0                                             /*set default for the @ stemmed array. */
#=0                                              /*number of narcissistic numbers so far*/
do p=0  for 39+1; if p<10  then call tell p /*display the 1st 1─digit dec. numbers.*/
do i=1  for 9;      @.p.i= i**p         /*build table of ten digits ^ P power. */
zzj= '00'j;       @.p.zzj= @.p.j        /*assign value for a 3-dig number (LZ),*/
end   /*i*/

do j=10  to 99;   parse var j  t 2 u    /*obtain 2 decimal digits of J:    T U */
@.p.j = @.p.t + @.p.u                   /*assign value for a 2─dig number.     */
zj=  '0'j;        @.p.zj = @.p.j        /*   "     "    "  " 3─dig    "   (LZ),*/
end   /*j*/                             /* [↑]  T≡ tens digit;  U≡ units digit.*/

do k=100  to 999; parse var k h 2 t 3 u /*obtain 3 decimal digits of J:  H T U */
@.p.k= @.p.h + @.p.t + @.p.u            /*assign value for a three-digit number*/
end   /*k*/                             /* [↑]  H≡ hundreds digit;  T≡ tens ···*/
end       /*p*/                             /* [↑]  table is a fixed (limited) size*/
/* [↓]  skip the 2─digit dec. numbers. */
do j=100;               L=length(j)         /*get length of the  J  decimal number.*/
parse var  j  _  +3  m                      /*get 1st three decimal digits of  J.  */
\$=@.L._                                     /*sum of the J decimal digs^L (so far).*/
do  while m\==''                 /*do the rest of the dec. digs in  J.  */
parse var  m    _  +3  m         /*get the next 3 decimal digits in  M. */
\$=\$ + @.L._                      /*add dec. digit raised to pow to sum. */
end   /*while*/                  /* [↑]  calculate the rest of the sum. */

if \$==j  then do;  call tell j              /*does the sum equal to  J?  Show the #*/
if #==n  then leave      /*does the sum equal to  J?  Show the #*/
end
end   /*j*/                                 /* [↑]  the  J loop  list starts at 100*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
tell: #=# + 1                                    /*bump the counter for narcissistic #s.*/
say right(#,9)   ' narcissistic:'   arg(1) /*display index and narcissistic number*/
if #==n  &  n<11  then exit                /*finished showing of narcissistic #'s?*/
```
output   is identical to the 1st REXX version.

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

## Ring

```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```

## Ruby

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

puts 0.step.lazy.select(&:narcissistic?).first(25)
```
Output:
```0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315
```

## Rust

```fn is_narcissistic(x: u32) -> bool {
let digits: Vec<u32> = x
.to_string()
.chars()
.map(|c| c.to_digit(10).unwrap())
.collect();

digits
.iter()
.map(|d| d.pow(digits.len() as u32))
.sum::<u32>()
== x
}

fn main() {
let mut counter = 0;
let mut i = 0;
while counter < 25 {
if is_narcissistic(i) {
println!("{}", i);
counter += 1;
}
i += 1;
}
}
```
Output:
```0
1
2
3
4
5
6
7
8
9
153
370
371
407
1634
8208
9474
54748
92727
93084
548834
1741725
4210818
9800817
9926315
```

## Scala

Works with: Scala version 2.9.x
```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(" "))

}
```

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

```func is_narcissistic(n) {
n.digits »**» n.len -> sum == n
}

var count = 0
for i in ^Inf {
if (is_narcissistic(i)) {
say "#{++count}\t#{i}"
break if (count == 25)
}
}
```
Output:
```1	0
2	1
3	2
4	3
5	4
6	5
7	6
8	7
9	8
10	9
11	153
12	370
13	371
14	407
15	1634
16	8208
17	9474
18	54748
19	92727
20	93084
21	548834
22	1741725
23	4210818
24	9800817
25	9926315
```

## Swift

```extension BinaryInteger {
@inlinable
public var isNarcissistic: Bool {
let digits = String(self).map({ Int(String(\$0))! })
let m = digits.count

guard m != 1 else {
return true
}

return digits.map({ \$0.power(m) }).reduce(0, +) == self
}

@inlinable
public func power(_ n: Self) -> Self {
return stride(from: 0, to: n, by: 1).lazy.map({_ in self }).reduce(1, *)
}

}

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

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

## Tcl

```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] ","]
```
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
```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"
```
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```

## Wren

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

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

## XPL0

This is based on Ring's version for Own Digits Power Sum.

```func IPow(A, B);        \A^B
int  A, B, T, I;
[T:= 1;
for I:= 1 to B do T:= T*A;
return T;
];

int Count, M, N, Sum, T, Dig;
[Text(0, "0 ");
Count:= 1;
for M:= 1 to 9 do
for N:= IPow(10, M-1) to IPow(10, M)-1 do
[Sum:= 0;
T:= N;
while T do
[T:= T/10;
Dig:= rem(0);
Sum:= Sum + IPow(Dig, M);
];
if Sum = N then
[IntOut(0, N);  ChOut(0, ^ );
Count:= Count+1;
if Count >= 25 then exit;
];
];
]```
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

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

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.

```var [const] powers=(10).pump(List,'wrap(n){
(1).pump(15,List,'wrap(p){ n.toFloat().pow(p).toInt() }) });
fcn isNarcissistic2(n){
m:=(n.numDigits - 1);
n.split().reduce('wrap(s,d){ s + powers[d][m] },0) == n
}```

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).

```ns:=[0..].filter.fp1(isNarcissistic);
ns(15).println();
ns(5).println();
ns(5).println();```
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)
```