a(n) = largest member of the n-th term in S(10) (defined in Comments).

Terms

a(0) =7a(1) =97a(2) =997a(3) =9973a(4) =99991a(5) =999983a(6) =294001a(7) =505447a(8) =584141a(9) =604171a(10) =929573a(11) =971767a(12) =9999991a(13) =1062599a(14) =1282529a(15) =1524181a(16) =2017963a(17) =2474431a(18) =2690201a(19) =3070663a(20) =3085553a(21) =3326489a(22) =4393139a(23) =5152507a(24) =5285767a(25) =5564453a(26) =5575259a(27) =5974249a(28) =6173731a(29) =6191371