a(n) and a(n)+4^k are primes at least for k=1,2,3,4,5,6,7,8.

Terms

a(0) =163a(1) =15667a(2) =607093a(3) =671353a(4) =1457857a(5) =5772097a(6) =9139453a(7) =11170933a(8) =13243063a(9) =18116473a(10) =19433863a(11) =21960577a(12) =32380177a(13) =52896517a(14) =115831753a(15) =154146133a(16) =165609217a(17) =191489677a(18) =361241743a(19) =394845313a(20) =518774953a(21) =613615423a(22) =705676717a(23) =742403797a(24) =786242293a(25) =945170293