A Disarium number is an integer where the sum of each digit raised to the power of its position in the number, is equal to the number.



E.G.
135 is a Disarium number:

 11 + 32 + 53 == 1 + 9 + 125 == 135

There are a finite number of Disarium numbers.



Task
 Find and display the first 18 Disarium numbers.


Stretch
 Find and display all 20 Disarium numbers.


See also
 Geeks for Geeks - Disarium numbers
 OEIS:A032799 - Numbers n such that n equals the sum of its digits raised to the consecutive powers (1,2,3,...)
 Related task: Narcissistic decimal number
 Related task: Own digits power sum Which seems to be the same task as Narcissistic decimal number...




use strict;
use warnings;
 
my ($n,@D) = (0, 0);
while (++$n) {
    my($m,$sum);
    map { $sum += $_ ** ++$m } split '', $n;
    push @D, $n if $n == $sum;
    last if 19 == @D;
}
print "@D\n";