a(n) = 2*a(n-1) + prime(n) - prime(n-1), a(1)=2, where prime(n) denotes the n-th prime.

Terms

a(0) =2a(1) =5a(2) =12a(3) =26a(4) =56a(5) =114a(6) =232a(7) =466a(8) =936a(9) =1878a(10) =3758a(11) =7522a(12) =15048a(13) =30098a(14) =60200a(15) =120406a(16) =240818a(17) =481638a(18) =963282a(19) =1926568a(20) =3853138a(21) =7706282a(22) =15412568a(23) =30825142a(24) =61650292a(25) =123300588a(26) =246601178a(27) =493202360a(28) =986404722a(29) =1972809448