The title says it all. Are there any special class of numbers other than $2^n$ for which Collatz is true? (I mean numbers such as other powers? or some other formula that is in essence not a manipulation of $2^n$. )
By the work of Ştefan Andrei, Manfred Kudlek, Radu Ştefan Niculescu, there are some more infinite sets of numbers for which the conjecture holds. There was a related question on MO here.
P.S. :Currently, the server I am using requires a subscription. I hope I will explain the details at a later date. If someone has access, please help.