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.


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] ","]