Collatz Primes

May 1, 2015

Today’s exercise comes from the world of recreational mathematics; I found it at Stack Overflow:

The Collatz sequence starting at n continues with n / 2, if n is even, and 3 n + 1 if n is odd. For instance, the Collatz sequence that starts from 19 is 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. It is conjectured that all Collatz sequences eventually end at 1, but has never been proven. The Collatz sequence that starts from 19 contains 7 prime numbers: 19, 29, 11, 17, 13, 5 and 2. Find the smallest starting number for a Collatz sequence that contains 65 or more primes.

Your task is to find the requested Collatz sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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