The whole set of coprime can be generated by two disjoint sets of ternary trees, one(red) from (2,1), and the other(blue) from (3,1). src
If the previous term is even, the next term is one half the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1.