a(1) = a(2) = 1; for n>2, a(n+1) = a(n) + a(n-1) iff a(n) is prime, otherwise a(n+1) = a(n) + 1.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =8a(6) =9a(7) =10a(8) =11a(9) =21a(10) =22a(11) =23a(12) =45a(13) =46a(14) =47a(15) =93a(16) =94a(17) =95a(18) =96a(19) =97a(20) =193a(21) =290a(22) =291a(23) =292a(24) =293a(25) =585a(26) =586a(27) =587a(28) =1173a(29) =1174