Interested with Python and Math, I have generalized 3n + 1 conjecture as 3n + 3^m conjecture ( m is any natural number) in 2014 :
Take any positive integer n. If n is even, divide it by 2 to get n / 2. If n is odd, multiply it by 3 and add 3^m to obtain 3n + 3^m. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 3^m.( When m = 0, it is 3n + 1 conjecture.)