OBM 1982 Problem 2

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