a(1)=2; for n>1 a(n) is the largest prime number m such that a(n-1)^(1/(n-1))>m^(1/n).

Terms

a(0) =2a(1) =3a(2) =5a(3) =7a(4) =11a(5) =17a(6) =23a(7) =31a(8) =47a(9) =71a(10) =107a(11) =163a(12) =241a(13) =367a(14) =557a(15) =839a(16) =1277a(17) =1933a(18) =2939a(19) =4463a(20) =6793a(21) =10337a(22) =15733a(23) =23929a(24) =36389a(25) =55381a(26) =84263a(27) =128239a(28) =195163a(29) =297023