Euler_14.py

# 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.


def check_number(number):
    if number % 2 == 0:
        return number//2
    return number*3 + 1


longestChain = 0
leader = 0

for number in range(2, 1000001):
    print(number)
    counter = 1
    temp = number
    while temp != 1:
        temp = check_number(temp)
        counter += 1
    if counter > longestChain:
        longestChain = counter
        leader = number
print("leader is ", leader)