Question 4
Any positive integer $n$ can be written in the form $n = 2^b(2c + 1)$. We call $2c + 1$ the *odd part of* $n$. Given an odd integer $n \gt 0$, define the sequence $a_0, a_1, a_2, \ldots$ as follows: $a_0 = 2^n - 1$, $a_{k+1}$ is the odd part of $3a_k + 1$. Find $a_n$.