A   Narcissistic decimal number   is a non-negative integer,   



n


{\displaystyle n}

,   that is equal to the sum of the   



m


{\displaystyle m}

-th   powers of each of the digits in the decimal representation of   



n


{\displaystyle n}

,   where   



m


{\displaystyle m}

   is the number of digits in the decimal representation of   



n


{\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   



n


{\displaystyle n}

   is   153 
   then   



m


{\displaystyle m}

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


Task

Generate and show here the first   25   narcissistic decimal numbers.



Note:   




0

1


=
0


{\displaystyle 0^{1}=0}

,   the first in the series.



See also

   the  OEIS entry:     Armstrong (or Plus Perfect, or narcissistic) numbers.
   MathWorld entry:   Narcissistic Number.
   Wikipedia entry:     Narcissistic number.


import sequtils, strutils
 
func digits(n: Natural): seq[int] =
  result.add n mod 10
  var n = n div 10
  while n != 0:
    result.add n mod 10
    n = n div 10
 
proc findNarcissistic(count: Natural): seq[int] =
  var
    n = 0
    m = 10
    powers = toseq(0..9)
  while true:
    while n < m:
      var s = 0
      for d in n.digits:
        inc s, powers[d]
      if s == n:
        result.add n
        if result.len == count: return
      inc n
    for i in 0..9: powers[i] *= i
    m *= 10
 
echo findNarcissistic(25).join(" ")