a(n) = (10^n + 53)/9.

Terms

a(0) =7a(1) =17a(2) =117a(3) =1117a(4) =11117a(5) =111117a(6) =1111117a(7) =11111117a(8) =111111117a(9) =1111111117a(10) =11111111117a(11) =111111111117