the williams numbers are also a generalization of thabit numbers. for integer "b" ≥ 2, a williams number base "b is a number of the form ("b"−1)·"b" − 1 for a non-negative integer "n". also, for integer "b" ≥ 2, a williams number of the second kind base "b is a number of the form ("b"−1)·"b" + 1 for a non-negative integer "n".