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.


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
]