a(1)=2, a(2)=3, a(3)=5; a(n) = largest prime < a(n-1)+a(n-2)+a(n-3).

Terms

a(0) =2a(1) =3a(2) =5a(3) =7a(4) =13a(5) =23a(6) =41a(7) =73a(8) =131a(9) =241a(10) =443a(11) =811a(12) =1493a(13) =2741a(14) =5039a(15) =9257a(16) =17033a(17) =31327a(18) =57601a(19) =105953a(20) =194869a(21) =358417a(22) =659237a(23) =1212521a(24) =2230159a(25) =4101907a(26) =7544573a(27) =13876601a(28) =25523011a(29) =46944179