Question 17
Let $a_1,$ $a_2,$ $\ldots$ be a sequence of integers determined by the rule $a_n = \frac{a_{n-1}}{2}$ if $a_{n-1}$ is even and $a_n = 3a_{n-1} + 1$ if $a_{n-1}$ is odd. For how many positive integers $a_1 \le 2008$ is it true that $a_1$ is less than each of $a_2,$ $a_3,$ and $a_4?$