a(n) = Sum_{i=1..n} 2^(b(i) - 1), where b(n) is the differences between consecutive primes.

Terms

a(0) =1a(1) =3a(2) =5a(3) =13a(4) =15a(5) =23a(6) =25a(7) =33a(8) =65a(9) =67a(10) =99a(11) =107a(12) =109a(13) =117a(14) =149a(15) =181a(16) =183a(17) =215a(18) =223a(19) =225a(20) =257a(21) =265a(22) =297a(23) =425a(24) =433a(25) =435a(26) =443a(27) =445a(28) =453a(29) =8645