# LONGEST COLLATZ SEQUENCE

"""
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 of the Collatz sequence?

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


def collatz_sequence(start_number):
    yield start_number
    while start_number != 1:
        if start_number % 2 == 0:
            start_number = start_number // 2
        else:
            start_number = 3 * start_number + 1
        yield start_number
        collatz_sequence(start_number)


def longest_collatz_sequence(limit=1000000):
    max = 1
    for i in range(limit, 1, -1):
        seq_len = len(list(collatz_sequence(i)))
        if seq_len > max:
            max = seq_len
            print("{} seq is of lentgh {}".format(i, seq_len))


if __name__ == "__main__":
    print(__doc__)
    print("*" * 70)
    longest_collatz_sequence(1000000)
