#!/usr/bin/perl
use 5.016;
use warnings;
 
# Farey sequence
# see: http://w...content-available-to-author-only...s.jp/ikuro_kotaro/koramu/1529_f2.htm
# see: http://m...content-available-to-author-only...m.com/FareySequence.html
# thanks: http://t...content-available-to-author-only...h.net/test/read.cgi/tech/1390525149/194
 
sub f {
	my ($n) = @_;
 
	return sub {
		my ($p, $q, $r, $s) = @_;
 
		my $pd = $p + $r;
		my $qd = $q + $s;
		($qd <= $n) or return ();
 
		return (
			__SUB__->($p, $q, $pd, $qd),
			"$pd/$qd",
			__SUB__->($pd, $qd, $r, $s)
		);
	}->(0, 1, 1, 1);
}
 
say join(' ', f(3));
say join(' ', f(5));
 

IyEvdXNyL2Jpbi9wZXJsCnVzZSA1LjAxNjsKdXNlIHdhcm5pbmdzOwoKIyBGYXJleSBzZXF1ZW5jZQojIHNlZTogaHR0cDovL3cuLi5jb250ZW50LWF2YWlsYWJsZS10by1hdXRob3Itb25seS4uLnMuanAvaWt1cm9fa290YXJvL2tvcmFtdS8xNTI5X2YyLmh0bQojIHNlZTogaHR0cDovL20uLi5jb250ZW50LWF2YWlsYWJsZS10by1hdXRob3Itb25seS4uLm0uY29tL0ZhcmV5U2VxdWVuY2UuaHRtbAojIHRoYW5rczogaHR0cDovL3QuLi5jb250ZW50LWF2YWlsYWJsZS10by1hdXRob3Itb25seS4uLmgubmV0L3Rlc3QvcmVhZC5jZ2kvdGVjaC8xMzkwNTI1MTQ5LzE5NAoKc3ViIGYgewoJbXkgKCRuKSA9IEBfOwoKCXJldHVybiBzdWIgewoJCW15ICgkcCwgJHEsICRyLCAkcykgPSBAXzsKCgkJbXkgJHBkID0gJHAgKyAkcjsKCQlteSAkcWQgPSAkcSArICRzOwoJCSgkcWQgPD0gJG4pIG9yIHJldHVybiAoKTsKCgkJcmV0dXJuICgKCQkJX19TVUJfXy0+KCRwLCAkcSwgJHBkLCAkcWQpLAoJCQkiJHBkLyRxZCIsCgkJCV9fU1VCX18tPigkcGQsICRxZCwgJHIsICRzKQoJCSk7Cgl9LT4oMCwgMSwgMSwgMSk7Cn0KCnNheSBqb2luKCcgJywgZigzKSk7CnNheSBqb2luKCcgJywgZig1KSk7Cg==