a(n) is smallest prime > 5*a(n-1), a(1) = 5.

Terms

a(0) =5a(1) =29a(2) =149a(3) =751a(4) =3761a(5) =18839a(6) =94201a(7) =471007a(8) =2355037a(9) =11775191a(10) =58875961a(11) =294379823a(12) =1471899119a(13) =7359495683a(14) =36797478433a(15) =183987392167a(16) =919936960849