Problem14.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.

# Rozwiązanie
chainmax=0
nmax=0
n=0
for i in range(2,1000000):
    chainl = 0
    n=i
    while n!=1:
        if n%2 == 0:
            n=n/2
        else:
            n=3*n+1
        chainl+=1
    if chainl>chainmax:
        chainmax=chainl
        nmax=i
print("Najdłuższy łańcuch o długości: ", chainmax, ", zostaje utworzony przez liczbę: ", nmax)