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

Terms

a(0) =7a(1) =37a(2) =163a(3) =757a(4) =967a(5) =1303a(6) =2293a(7) =2377a(8) =8677a(9) =8803a(10) =9157a(11) =9277a(12) =14827a(13) =15667a(14) =16417a(15) =20113a(16) =27763a(17) =29863a(18) =41953a(19) =53593a(20) =56527a(21) =56893a(22) =61027a(23) =67153a(24) =69763a(25) =74827a(26) =79333a(27) =83203a(28) =90007a(29) =95467