A045538 Smallest number k such that kn contains two consecutive digits which are the same.

11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 1, 12, 9, 8, 15, 7, 7, 8, 6, 5, 16, 1, 5, 6, 4, 13, 37, 4, 4, 10, 5, 7, 1, 13, 13, 4, 3, 3, 3, 5, 13, 8, 8, 1, 5, 7, 4, 3, 9, 2, 5, 17, 9, 21, 1, 2, 2, 2, 2, 5, 2, 9, 7, 7, 7, 1, 5, 8, 8, 10, 5, 2, 7, 3, 3, 3, 1, 15, 7, 5, 14, 13, 2, 4, 3, 4, 6, 1, 5, 10, 5