Non-adding primes: next term is smallest prime not the sum of any primes so far.

Terms

a(0) =2a(1) =3a(2) =7a(3) =11a(4) =17a(5) =41a(6) =47a(7) =83a(8) =89a(9) =307a(10) =311a(11) =613a(12) =617a(13) =919a(14) =2801a(15) =3109a(16) =3413a(17) =9283a(18) =15461a(19) =25087a(20) =37781a(21) =87613a(22) =106181a(23) =284509a(24) =296591a(25) =618269a(26) =1196609a(27) =1774921a(28) =3564677a(29) =5339287