a(n) is the least positive integer such that nextprime(a(n)^n) - prevprime(a(n)^n) = 4.

Terms

a(0) =5a(1) =3a(2) =2a(3) =2a(4) =411a(5) =195a(6) =2a(7) =392a(8) =141a(9) =105a(10) =1161a(11) =909a(12) =69a(13) =3243a(14) =171a(15) =370a(16) =1659a(17) =165a(18) =26289a(19) =1065a(20) =8541a(21) =19593a(22) =43521a(23) =1323a(24) =84651a(25) =25767a(26) =25641a(27) =7029a(28) =63009a(29) =693