a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6,7.

Terms

a(0) =37a(1) =163a(2) =15667a(3) =142543a(4) =607093a(5) =671353a(6) =1457857a(7) =2694157a(8) =2979043a(9) =4890307a(10) =5772097a(11) =6404773a(12) =9139453a(13) =10669003a(14) =11170933a(15) =11218747a(16) =11905987a(17) =13243063a(18) =15130537a(19) =18116473a(20) =19433863a(21) =21960577a(22) =23524183a(23) =25946083a(24) =32380177a(25) =45600157a(26) =46960747a(27) =51905137