a(n) is the largest prime that is a sum of some 3 distinct previous terms.

Terms

a(0) =5a(1) =7a(2) =11a(3) =23a(4) =41a(5) =71a(6) =101a(7) =179a(8) =257a(9) =443a(10) =521a(11) =971a(12) =1499a(13) =2477a(14) =2927a(15) =3191a(16) =3719a(17) =6917a(18) =9851a(19) =13577a(20) =16061a(21) =25919a(22) =39503a(23) =53087a(24) =56813a(25) =96323a(26) =149417a(27) =245747a(28) =342077a(29) =491501