Largest prime < 10*a(n-1), a(1)=3.

Terms

a(0) =3a(1) =29a(2) =283a(3) =2819a(4) =28183a(5) =281807a(6) =2818043a(7) =28180393a(8) =281803927a(9) =2818039241a(10) =28180392407a(11) =281803924067