a(1) = 1; a(n) = prime((a(n-1)+3)/2).

Terms

a(0) =1a(1) =3a(2) =5a(3) =7a(4) =11a(5) =17a(6) =29a(7) =53a(8) =107a(9) =257a(10) =733a(11) =2503a(12) =10211a(13) =49739a(14) =285377a(15) =1909561a(16) =14736529a(17) =129812899a(18) =1293238351a(19) =14448382721a(20) =179668662139