a(n) = prime((a(n-1) + 1)/2), a(1) = 21.

Terms

a(0) =21a(1) =31a(2) =53a(3) =103a(4) =239a(5) =659a(6) =2213a(7) =8887a(8) =42473a(9) =240151a(10) =1584607a(11) =12069311a(12) =105036509a(13) =1034651039a(14) =11438277847a(15) =140842283467