DouKaku?

#!/usr/local/bin/perl

use strict;
use warnings;

my $max = 10000;

for ( my $orig = 10; $orig <= $max; $orig++ ) {

        print ".";

        my $num13 = 0;
        my $length = 0;

        my $orig_tmp = $orig;
        while( $orig_tmp ) {
                $num13 += ( 13 ** $length ) *  ( $orig_tmp % 10 );
                $orig_tmp = int ( $orig_tmp / 10 );
                $length++;
        }

        if( $num13 % $orig == 0 ) {
                print "\nFound: $orig => $num13\n";
                exit 0;
        }
}