a(n) = (2^(n-1) + prime(n+1)-prime(n))/2.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =9a(5) =18a(6) =33a(7) =66a(8) =131a(9) =257a(10) =515a(11) =1026a(12) =2049a(13) =4098a(14) =8195a(15) =16387a(16) =32769a(17) =65539a(18) =131074a(19) =262145a(20) =524291a(21) =1048578a(22) =2097155a(23) =4194308a(24) =8388610a(25) =16777217a(26) =33554434a(27) =67108865a(28) =134217730a(29) =268435463