(nextprime(5^n)-nextprime(2^n))/2.

Terms

a(0) =0a(1) =2a(2) =12a(3) =58a(4) =307a(5) =1550a(6) =7781a(7) =39003a(8) =195195a(9) =976315a(10) =4882299a(11) =24413043a(12) =122068292a(13) =610347461a(14) =3051749613a(15) =15258772698a(16) =76293912556a(17) =381469661013