The Modern C++ Challenge

12. Largest Collatz sequence

The Collatz conjecture, also known as the Ulam conjecture, Kakutani's problem, the Thwaites conjecture, Hasse's algorithm, or the Syracuse problem, is an unproven conjecture that states that a sequence defined as explained in the following always reaches 1. The series is defined as follows: start with any positive integer n and obtain each new term from the previous one: if the previous term is even, the next term is half the previous term, or else it is 3 times the previous term plus 1.

The problem you are to solve is to generate the Collatz sequence for all positive integers up to one million, determine which of them is the longest, and print its length and the starting number that produced it. Although we could ...