A super-d number is a positive, decimal (base ten) integer   n   such that   d × nd   has at least   d   consecutive digits   d   where

   2 ≤ d ≤ 9

For instance, 753 is a super-3 number because 3 × 7533 = 1280873331.


Super-d   numbers are also shown on   MathWorld™   as   super-d    or   super-d.



Task

 Write a function/procedure/routine to find super-d numbers.
 For   d=2   through   d=6,   use the routine to show the first   10   super-d numbers.


Extra credit

 Show the first   10   super-7, super-8, and/or super-9 numbers   (optional).


See also

   Wolfram MathWorld - Super-d Number.
   OEIS: A014569 - Super-3 Numbers.


use strict;
use warnings;
use bigint;
use feature 'say';
 
sub super {
    my $d = shift;
    my $run = $d x $d;
    my @super;
    my $i = 0;
    my $n = 0;
    while ( $i < 10 ) {
        if (index($n ** $d * $d, $run) > -1) {
            push @super, $n;
            ++$i;
        }
        ++$n;
    }
    @super;
}
 
say "\nFirst 10 super-$_ numbers:\n", join ' ', super($_) for 2..6;