Let a(1)=1; for n>1, a(n)=nextprime( a(n-1)^(n/(n-1)) ).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =11a(5) =19a(6) =37a(7) =67a(8) =127a(9) =223a(10) =383a(11) =659a(12) =1151a(13) =1987a(14) =3433a(15) =5923a(16) =10211a(17) =17579a(18) =30259a(19) =52103a(20) =89689a(21) =154387a(22) =265747a(23) =457421a(24) =787357a(25) =1355261a(26) =2332783a(27) =4015339a(28) =6911461a(29) =11896457