a(n) is the smallest odd prime of the form ((1 + sqrt(2*n))^k - (1 - sqrt(2*n))^k)/(2*sqrt(2*n)).

Terms

a(0) =5a(1) =7a(2) =101a(3) =11a(4) =13a(5) =269a(6) =17a(7) =19a(8) =509a(9) =23a(10) =709a(11) =821a(12) =29a(13) =31a(14) =46957a(15) =55399a(16) =37a(17) =168846239a(18) =41a(19) =43a(21) =47a(22) =485329129a(23) =2789a(24) =53a(25) =3229a(26) =3461a(27) =59a(28) =61a(29) =1563353111a(30) =139237612541