a(n) is the number of subsets of the first n primes whose sum is not a prime.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =9a(5) =20a(6) =44a(7) =93a(8) =191a(9) =390a(10) =787a(11) =1600a(12) =3250a(13) =6563a(14) =13227a(15) =26609a(16) =53484a(17) =107588a(18) =216413a(19) =434894a(20) =872834a(21) =1750938a(22) =3512454a(23) =7043770a(24) =14119562a(25) =28300792a(26) =56733873a(27) =113746102a(28) =228033527a(29) =456999525