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$n >> 1;

    while ($n != 1) {
        $result += $cache[$n], last
...

        $n = $new_n;
    }

    while ($n != 1) {
        $result += $cache[$n], last
...

        $n = $new_n;
    }

    while ($n != 1) {
        $result += $cache[$n], last
...

        $n = $new_n;
    }

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

@long_seqs = sort { $b->[1] <=> $a->[1]} @long_seqs;
say "$_->[0]: $_->[1]" for @long_seqs[0..19];

$ time perl collatz3_a.pl 1e7

...
5598635: 595
8397953: 593
6298465: 590