Your loop in the totalizer-sub is very unusual.

I would write this sub like this:

sub totalizer {
    my $number = shift;

    my $cycle_length = 1;

    while($number != 1) {
        $cycle_length++;

        $number = $number % 2  ? $number * 3 + 1
                               : $number / 2;

    }
    return $cycle_length;
}
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