A special sequence - Lycée Arago (Perpignan) Colegiul National B.P. Hasdeu (Buzau, Roumanie)

A sequence of integers is defined by a_1=2,a_2=3 and, for each n≥2:
either a_(n+1)=2a_(n-1) or a_(n+1)=3a_n-2a_(n-1).
Can that sequence reach any of the following numbers: 17 ?21 ?1600?1536 ?2017 ?