a(1) = 2; a(n) is the smallest prime greater than the sum of all previous terms.

Terms

a(0) =2a(1) =3a(2) =7a(3) =13a(4) =29a(5) =59a(6) =127a(7) =241a(8) =487a(9) =971a(10) =1949a(11) =3889a(12) =7789a(13) =15569a(14) =31139a(15) =62297a(16) =124577a(17) =249181a(18) =498331a(19) =996689a(20) =1993357a(21) =3986711a(22) =7973419a(23) =15946841a(24) =31893713a(25) =63787391a(26) =127574789a(27) =255149591a(28) =510299171a(29) =1020598339