a(n) is smallest prime > 2*a(n-1), a(1) = 3.

Terms

a(0) =3a(1) =7a(2) =17a(3) =37a(4) =79a(5) =163a(6) =331a(7) =673a(8) =1361a(9) =2729a(10) =5471a(11) =10949a(12) =21911a(13) =43853a(14) =87719a(15) =175447a(16) =350899a(17) =701819a(18) =1403641a(19) =2807303a(20) =5614657a(21) =11229331a(22) =22458671a(23) =44917381a(24) =89834777a(25) =179669557a(26) =359339171a(27) =718678369a(28) =1437356741a(29) =2874713497