a(n) = (10^n + 17)/9.

Terms

a(0) =2a(1) =3a(2) =13a(3) =113a(4) =1113a(5) =11113a(6) =111113a(7) =1111113a(8) =11111113a(9) =111111113a(10) =1111111113a(11) =11111111113a(12) =111111111113