# zbMATH — the first resource for mathematics

Multiples of repunits as sum of powers of ten. (English) Zbl 1300.11014
Summary: The sequence $$P_{k,n}=1+10^k+10^{2k}+\cdots+10^{(n-1)k}$$ 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 $$k\geqslant 9$$. This fact complements the earlier results which have been established for $$k\leqslant 9$$.
##### MSC:
 11A63 Radix representation; digital problems
##### Keywords:
repunits; Smith numbers
Full Text:
##### References:
 [1] McDaniel, W. L., The existence of infinitely many k-Smith numbers, Fibonacci Quart., 25, 76-80, (1987) · Zbl 0608.10012 [2] Wilansky, A., Smith numbers, Two-Year College Math. J., 13, 21, (1982) [3] Witno, A., A family of sequences generating Smith numbers, J. Integer Seq., 16, (2013), Art. 13.4.6 · Zbl 1285.11020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.