a(n) = prime((a(n-1) + 1)/2), a(1) = 15.

Terms

a(0) =15a(1) =19a(2) =29a(3) =47a(4) =89a(5) =197a(6) =523a(7) =1667a(8) =6397a(9) =29437a(10) =160423a(11) =1023227a(12) =7552957a(13) =63845779a(14) =612095179a(15) =6597973097a(16) =79345496843