a(1)=2; a(n)=smallest prime not less than the sum of all previous terms.

Terms

a(0) =2a(1) =2a(2) =5a(3) =11a(4) =23a(5) =43a(6) =89a(7) =179a(8) =359a(9) =719a(10) =1433a(11) =2879a(12) =5749a(13) =11497a(14) =22993a(15) =45989a(16) =91997a(17) =183971a(18) =367949a(19) =735901a(20) =1471807a(21) =2943599a(22) =5887213a(23) =11774429a(24) =23548853a(25) =47097697a(26) =94195421a(27) =188390809a(28) =376781623a(29) =753563269