a(n) = (5*10^n + 13)/9.

Terms

a(0) =2a(1) =7a(2) =57a(3) =557a(4) =5557a(5) =55557a(6) =555557a(7) =5555557a(8) =55555557a(9) =555555557a(10) =5555555557a(11) =55555555557a(12) =555555555557