DK-GEORGMOHR 2025 Problem 5

Georg plays the following game. He chooses a positive integer $n$ , which he writes on a board. In each move Georg does the following: If the number $m$ written on the board is even, he replaces $m$ by $\frac{m}{2}$ . If the number $m$ written on the board is odd, he replaces $m$ by $m^2 + 3$ . Georg wins if he after a finite number of moves writes the number $n$ on the board again. For which positive integers n does Georg win?