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

Terms

a(0) =2a(1) =2a(2) =7a(3) =29a(4) =71a(5) =73a(6) =251a(7) =149a(8) =751a(9) =1013a(10) =1103a(11) =1201a(12) =2399a(13) =1697a(14) =2659a(15) =4397a(16) =2999a(17) =5101a(18) =5303a(19) =6361a(20) =8039a(21) =8861a(22) =8563a(23) =15773a(24) =11783a(25) =17117a(26) =13159a(27) =30941a(28) =25703a(29) =35801