a(1) = 2; a(n) = largest prime not exceeding the sum of all previous terms.

Terms

a(0) =2a(1) =3a(2) =5a(3) =7a(4) =17a(5) =31a(6) =61a(7) =113a(8) =239a(9) =467a(10) =941a(11) =1879a(12) =3761a(13) =7523a(14) =15031a(15) =30071a(16) =60149a(17) =120299a(18) =240599a(19) =481181a(20) =962363a(21) =1924721a(22) =3849437a(23) =7698893a(24) =15397783a(25) =30795571a(26) =61591147a(27) =123182281a(28) =246364571a(29) =492729101