Let $a_1,a_2,\dots$ be a sequence determined by the rule $a_n=a_{n-1}/3$ if $a_{n-1}$ is a multiple of 3 and $a_n=2a_{n-1}+1$ if $a_{n-1}$ is not a multiple of 3. For how many positive integers $a_1\le 1000$ is it true that $a_1$ is less than each of $a_2$ and $a_3$?