Let a(1)=1; for n>1 a(n)=nextprime(a(n-1)+(a(n-1)+1)/4).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =7a(5) =11a(6) =17a(7) =23a(8) =29a(9) =37a(10) =47a(11) =59a(12) =79a(13) =101a(14) =127a(15) =163a(16) =211a(17) =269a(18) =337a(19) =431a(20) =541a(21) =677a(22) =853a(23) =1069a(24) =1361a(25) =1709a(26) =2137a(27) =2677a(28) =3347a(29) =4201