#14 longest collatz sequence

"""
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?

https://projecteuler.net/problem=14
"""

def collatz(seq_lst, n):
    # append starting value
    seq_lst.append(int(n))
    while n > 1:
        # even
        if n % 2 == 0:
            n = n / 2
            seq_lst.append(int(n))
        # odd
        else:
            n = 3 * n + 1
            seq_lst.append(int(n))

    return seq_lst

assert collatz([], 13) == [13, 40, 20, 10, 5, 16, 8, 4, 2, 1]

# solution (slow)

MAX_RANGE = 1000000

longest = (0, 0)

for n in range(MAX_RANGE):
    seq = collatz([], n)
    if len(seq) > longest[1]:
        longest = (n, len(seq))

print(longest[0])
# 837799