Re^4: Challenge: Another Infinite Lazy List

[Roy Johnson]

Here's a filter that is O(F=number of factors * P=product of factors) + O(N) to check N numbers. It takes advantage of the fact that the output is periodic: if N is a member, then N + P is also a member. This could be written caching-style, so you only have to do your gcd check if you don't yet have a result for N % P; that would improve your order of efficiency without the potential big up-front cost.

use strict; 
use warnings;

{
    my @bases = (2,3,5);
    my $product = 1;
    $product *= $_ for @bases;
    my @key;
    for my $test (0..$product-1) {
        $key[$test] = grep {$test % $_ == 0} @bases;
    }
    print "Key is <@key>\n";
    my $iteration = 1;
    sub limbic_sequence {
        $iteration = shift if (@_); 
        while ($iteration++) {
            return $iteration if ($key[$iteration % @key]);
        }
    }
}

print join ', ', map limbic_sequence, 1..50;
print "\n";
printf "First after 100000 is: %d\n", limbic_sequence(100000);
print join ', ', map limbic_sequence, 1..50;
print "\n";