a(1) = 2; a(n) is the smallest prime > a(n-1) such that a(n) + a(n-1) is a square.

Terms

a(0) =2a(1) =7a(2) =29a(3) =71a(4) =73a(5) =251a(6) =773a(7) =827a(8) =937a(9) =1367a(10) =1549a(11) =5507a(12) =7489a(13) =8387a(14) =8513a(15) =10531a(16) =11969a(17) =16931a(18) =18413a(19) =18451a(20) =20753a(21) =21683a(22) =24113a(23) =25171a(24) =26813a(25) =27011a(26) =29633a(27) =33871a(28) =63473a(29) =76403