290237644800000000000000000000000000000
290420756304773155911401472000000000000
290469810882260083566182400000000000000
290565366750000000000000000000000000000
290748685015200298451950845000000000000


##</code><code>##

use strict; 
use warnings;
use Math::BigInt;
{
    my @history = (Math::BigInt->new('1'));
    my @streams = map {base => $_, index => 0}, (2, 3, 5);
    sub print_status {
        print "$_->{base}: $_->{index}\n" for @streams;
        print "History is " . @history . " elements\n";
    }
    sub ham_iter {
        # Make sure all stream indexes are > 0
        while ($streams[2]{index} == 0) {
            # Find the next lowest value to push onto history
            my @peeks = map {
                $history[$_->{index}]->copy()->bmul($_->{base})
            } @streams;
            my ($lowest) = sort {$a->bcmp($b)} @peeks;
            $peeks[$_]->bcmp($lowest) or $streams[$_]{index}++ for 0..$#streams;
            push(@history, $lowest);
        }
        # Now adjust all the indexes for the element being removed
        $_->{index}-- for @streams;
        shift @history;
    }
}
# Skipping however many
ham_iter() for (1..10);
# Then print the next five
print ham_iter->bstr(), "\n" for (1..5);
# Then tell us about what's stored
print_status();