a(n) is smallest prime > 3*a(n-1), a(1) = 3.

Terms

a(0) =3a(1) =11a(2) =37a(3) =113a(4) =347a(5) =1049a(6) =3163a(7) =9491a(8) =28477a(9) =85439a(10) =256337a(11) =769019a(12) =2307059a(13) =6921179a(14) =20763541a(15) =62290633a(16) =186871907a(17) =560615723a(18) =1681847191a(19) =5045541577a(20) =15136624739a(21) =45409874221a(22) =136229622677a(23) =408688868051