Palindromes are neat.
Palindromic numbers in base 10 as well as base 2 are even more neat!
Enter a max value and it'll do the rest.
(note: Base10 is human-readable numbers, where Base2 is binary)

#!/usr/bin/perl
use warnings;
use strict;

my $sum;
print "Max value: ";
my $length = <STDIN>;

for(my $i=1; $i<$length; $i++) {
    my $bnum = sprintf("%b", $i);
    if ($i == reverse($i)
    && $bnum == reverse($bnum)) {
        print "$i:$bnum\n";
    }
}