a(3) = 2, a(4) = 3; for n > 4, a(n) = {a(n-2)}+{a(n-1)}, where {a} means largest prime <= a.

Terms

a(0) =2a(1) =3a(2) =5a(3) =8a(4) =12a(5) =18a(6) =28a(7) =40a(8) =60a(9) =96a(10) =148a(11) =228a(12) =366a(13) =586a(14) =936a(15) =1506a(16) =2428a(17) =3922a(18) =6342a(19) =10256a(20) =16590a(21) =26826a(22) =43394a(23) =70212a(24) =113598a(25) =183798a(26) =297388a(27) =481174a(28) =778548a(29) =1259712