OMM 2003 Problem 6

Given a positive integer $n$ , an allowed move is to form $2n+1$ or $3n+2$ . The set $S_{n}$ is the set of all numbers that can be obtained by a sequence of allowed moves starting with $n$ . For example, we can form $5 \rightarrow 11 \rightarrow 35$ so $5, 11$ and $35$ belong to $S_{5}$ . We call $m$ and $n$ compatible if $S_{m}$ and $S_{n}$ has a common element. Which members of $\{1, 2, 3, ... , 2002\}$ are compatible with $2003$ ?