2008 AMC 12A Problem 17

Let a_1,a_2,\ldots be a sequence determined by the rule a_n=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?

\mathrm{(A)}\ 250\qquad\mathrm{(B)}\ 251\qquad\mathrm{(C)}\ 501\qquad\mathrm{(D)}\ 502\qquad\mathrm{(E)} 1004

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.