014.js

// The following iterative sequence is defined for the set of positive integers:

//   n → n/2 (n is even)
//   n → 3n + 1 (n is odd)

// Using the rule above and starting with 13, we generate the following 
// sequence:
//   13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1

// It can be seen that this sequence (starting at 13 and finishing at 1) 
// contains 10 terms. Although it has not been proved yet (Collatz Problem), it 
// is thought that all starting numbers finish at 1.

// Which starting number, under one million, produces the longest chain?

// NOTE: Once the chain starts the terms are allowed to go above one million.

function collatz(n) {
	var chain = [];
	while (n !== 1) {
		chain.push(n);
		if (n%2 === 0) {
			n = n/2;
		} else {
			n = 3*n + 1;
		}
	}
	chain.push(1);
	return chain;
}

function longestChain(max) {
	var longest = 1;
	var number = 1;
	var chain;
	for (var i = 1; i <= max; i++) {
		chain = collatz(i);
		if (chain.length > longest) {
			number = i;
			longest = chain.length;
		}
	}
	return number;
}

console.log( longestChain(1000000) );