a(0)=1, a(1)=2, a(n) = largest prime < a(n-1)+a(n-2).

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =3a(5) =5a(6) =7a(7) =11a(8) =17a(9) =23a(10) =37a(11) =59a(12) =89a(13) =139a(14) =227a(15) =359a(16) =577a(17) =929a(18) =1499a(19) =2423a(20) =3919a(21) =6337a(22) =10253a(23) =16573a(24) =26821a(25) =43391a(26) =70207a(27) =113591a(28) =183797a(29) =297377