Question 4
Any positive integer $n$ can be written in the form $n=2^aq$, where $a\ge0$ and $q$ is odd. We call $q$ the odd part of $n$. Define the sequence $a_0,a_1,\ldots$ as follows: $a_0=2^{2011}-1$ and for $m\ge0$, $a_{m+1}$ is the odd part of $3a_m+1$. Find $a_{2011}$.