Define g(k) = min(n: n >= 0, 2^n + k prime). Then a(n) = min(odd k: g(k) = n).

Terms

a(0) =1a(1) =3a(2) =7a(3) =23a(4) =31a(5) =47a(6) =199a(7) =83a(8) =61a(9) =257a(10) =139a(11) =953a(12) =991a(13) =647a(14) =1735a(15) =383a(16) =511a(17) =1337a(18) =1069a(19) =713a(20) =271a(21) =1937a(22) =3223a(23) =5213a(24) =751a(25) =8477a(26) =4339a(27) =353a(28) =1501a(29) =287