a(1) = 1, a(n+1) = least prime p > a(n) such that a(n) + p is a square.

Terms

a(0) =1a(1) =3a(2) =13a(3) =23a(4) =41a(5) =59a(6) =137a(7) =263a(8) =313a(9) =587a(10) =709a(11) =2207a(12) =2417a(13) =2767a(14) =4289a(15) =4547a(16) =5857a(17) =8543a(18) =9413a(19) =9631a(20) =18593a(21) =20611a(22) =45953a(23) =50147a(24) =52253a(25) =55331a(26) =58913a(27) =62191a(28) =67409a(29) =69491