# A Collatz like problem

Prove or disprove:

Let $a_0$ be any positive integer,defining:

$$a_{n+1} = \begin{cases}\frac{a_n}{2} &, a_n \text{ even}\\ 3a_n - 1 &, a_n \text{ odd}. \end{cases}$$

Then $a_k=1,7$ or $17$(all of them forms loops) where $k$ is some integer....

It is not known if those three cycles are the only cycles nor if every sequence ends up in a cycle instead of diverging to $- \infty$
• The Collatz problem terminates at $1$, how is this the same thing? – Hashir Omer May 13 '14 at 9:57
• @HashirOmer The Collatz problems starting at any negative integer (like $-1,-7$ or $-17$) don't terminate at $1$. – mercio May 13 '14 at 10:21