a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6.

Terms

a(0) =37a(1) =163a(2) =15667a(3) =53593a(4) =142543a(5) =305407a(6) =607093a(7) =671353a(8) =904663a(9) =1172803a(10) =1233523a(11) =1351837a(12) =1378843a(13) =1389217a(14) =1457857a(15) =1686133a(16) =1842523a(17) =1867783a(18) =2451793a(19) =2668213a(20) =2694157a(21) =2979043a(22) =3095227a(23) =4228723a(24) =4890307a(25) =5535853a(26) =5772097a(27) =5859613a(28) =6404773a(29) =6827503