The sequence P k , n = 1 + 10 k + 10 2 k + ? + 10 ( n ?1) k can be used to generate infinitely many Smith numbers with the help of a set of suitable multipliers. We prove the existence of such a set, consisting of constant multiples of repunits, that generalizes to any value of k ? 9. This fact complements the earlier results which have been established for k ? 9.
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机译：序列P k，n = 1 + 10 k + 10 2 k +？借助于一组合适的乘数，可以使用+ 10（n？1）k生成无限多个史密斯数。我们证明了存在这样一个集合，该集合由repunits的常数倍组成，可以推广到k的任何值。 9.这一事实是对k？的较早结果的补充。 9。
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