Sum_{k=1..n} (-1)^isprime(k)*2^k.

Terms

a(0) =2a(1) =-2a(2) =-10a(3) =6a(4) =-26a(5) =38a(6) =-90a(7) =166a(8) =678a(9) =1702a(10) =-346a(11) =3750a(12) =-4442a(13) =11942a(14) =44710a(15) =110246a(16) =-20826a(17) =241318a(18) =-282970a(19) =765606a(20) =2862758a(21) =7057062a(22) =-1331546a(23) =15445670a(24) =49000102a(25) =116108966a(26) =250326694a(27) =518762150a(28) =-18108762a(29) =1055633062