As some of the people have already said, this is the Collatz conjecture aka 3n+1 problem aka half-or-triple-plus-one (HOTPO)problem. The fact that we don't know

As some of the people have already said, this is the Collatz conjecture aka 3n+1 problem aka half-or-triple-plus-one (HOTPO)problem. The fact that we don't know if the algorithm will certainly land on a power of two shows that it's quite a difficult problem. The famous mathematician Erdos said that math is not yet ready for such problems. There are heuristic to show that the algorithm should terminate but there are numbers for which it takes an arbitrarily long time for convergence. Furthermore, there are similar problems that have divergence or loops. What makes matters worse is that it's been proven that such problems are undecidable in general.