a(n) = p-n!, where p is the smallest prime > n!+1.

Terms

a(0) =2a(1) =3a(2) =5a(3) =5a(4) =7a(5) =7a(6) =11a(7) =23a(8) =17a(9) =11a(10) =17a(11) =29a(12) =67a(13) =19a(14) =43a(15) =23a(16) =31a(17) =37a(18) =89a(19) =29a(20) =31a(21) =31a(22) =97a(23) =131a(24) =41a(25) =59a(26) =47a(27) =67a(28) =223a(29) =107