NL-NWO 1994 Problem 2

A sequence of integers $a_1,a_2,a_3,...$ is such that $a_1=2, a_2=3$ , and

$a_{n+1}=2a_{n-1}$ or $3a_n-2a_{n-1}$ for all $n \ge 2$ .

Prove that no number between $1600$ and $2000$ can be an element of the sequence.