(Prime(n)# - 4)/2 is prime, where x# is the primorial A034386(x).

Terms

a(0) =3a(1) =4a(2) =5a(3) =6a(4) =7a(5) =8a(6) =9a(7) =11a(8) =13a(9) =16a(10) =20a(11) =27a(12) =39a(13) =83a(14) =103a(15) =122a(16) =129a(17) =145a(18) =279a(19) =393a(20) =608a(21) =798a(22) =929a(23) =1164a(24) =1266a(25) =1491a(26) =2043a(27) =3276a(28) =3426a(29) =7119