BG-MO 2002 Problem 5

Find all pairs $(b,c)$ of positive integers, such that the sequence defined by $a_1=b$ , $a_2=c$ and $a_{n+2}= \left| 3a_{n+1}-2a_n \right|$ for $n \geq 1$ has only finite number of composite terms.

Proposed by Oleg Mushkarov and Nikolai Nikolov