<?php

#2. The Collatz conjecture:
#Given a positive integer n, form a sequence by iteratively performing the
#following operations:
#	If n is even, divide by 2.
#	If n is odd, multiply by 3 and add 1.
#The sequence stops when n is equal to 1. It is believed (but not yet proven)
#that regardless of the starting number, all sequences end at 1.
#For starting numbers less than 100, find the length of the longest sequence.

function collatz($start) {
	$count = 1;
	while ($start != 1) {
		if ($start % 2 == 0) {
			$start /= 2;
		} else {
			$start = $start*3 + 1;
		}
		$count++;
	}
	return $count;
}

$maxLen = 0;
$maxNum = 0;
for ($i = 1; $i < 100; $i++) {
	$result = collatz($i);
	if ($result > $maxLen) {
		$maxLen = $result;
		$maxNum = $i;
	}
}

echo "The longest chain starts at $maxNum and has length = $maxLen.\n";

?>