The Jacobsthal sequence, dropping each third term.

Terms

a(0) =1a(1) =1a(2) =5a(3) =11a(4) =43a(5) =85a(6) =341a(7) =683a(8) =2731a(9) =5461a(10) =21845a(11) =43691a(12) =174763a(13) =349525a(14) =1398101a(15) =2796203a(16) =11184811a(17) =22369621a(18) =89478485a(19) =178956971a(20) =715827883a(21) =1431655765a(22) =5726623061a(23) =11453246123a(24) =45812984491a(25) =91625968981a(26) =366503875925a(27) =733007751851