a(n) = (nextprime(4^n) - nextprime(2^n))/2.

Terms

a(0) =0a(1) =1a(2) =6a(3) =28a(4) =120a(5) =497a(6) =2016a(7) =8140a(8) =32640a(9) =130813a(10) =523776a(11) =2096133a(12) =8386580a(13) =33550335a(14) =134209524a(15) =536854528a(16) =2147450887a(17) =8589869054a(18) =34359607310a(19) =137438691321a(20) =549755289604