a(n) is the largest prime of the form x^2 + 1 <= 2^n.

Terms

a(0) =2a(1) =2a(2) =5a(3) =5a(4) =17a(5) =37a(6) =101a(7) =197a(8) =401a(9) =677a(10) =1601a(11) =3137a(12) =8101a(13) =15877a(14) =32401a(15) =62501a(16) =122501a(17) =246017a(18) =512657a(19) =1020101a(20) =2073601a(21) =4137157a(22) =8386817a(23) =16695397a(24) =33339077a(25) =66977857a(26) =133772357a(27) =268304401a(28) =536663557a(29) =1073610757