def collatz_sequence(n):
    """Collatz conjecture: start with any positive integer n.Next termis obtained from the previous term as follows:
    if the previous term is even, the next term is one half the previous term.
    If the previous term is odd, the next term is 3 times the previous term plus 1.
    The conjecture states the sequence will always reach 1 regaardess of starting n."""
    sequence = [n]
    while n != 1:
        if n % 2 == 0:  # even
            n //= 2
        else:
            n = 3 * n + 1
        sequence.append(n)
    return sequence


answer = max([(len(collatz_sequence(i)), i) for i in range(1, 1000000)])
print("Longest Collatz sequence under one million is %d with length %d" % (answer[1], answer[0]))
