ISL 1994 N4

Define the sequences $a_n, b_n, c_n$ as follows. $a_0 = k, b_0 = 4, c_0 = 1$ . If $a_n$ is even then $a_{n + 1} = \frac {a_n}{2}$ , $b_{n + 1} = 2b_n$ , $c_{n + 1} = c_n$ . If $a_n$ is odd, then $a_{n + 1} = a_n - \frac {b_n}{2} - c_n$ , $b_{n + 1} = b_n$ , $c_{n + 1} = b_n + c_n$ . Find the number of positive integers $k < 1995$ such that some $a_n = 0$ .