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- W2892095864 abstract "For an integer $b geqslant 2$ and a set $Ssubset {0,cdots,b-1}$, we define the Kempner set $mathcal{K}(S,b)$ to be the set of all non-negative integers whose base-$b$ digital expansions contain only digits from $S$. These well-studied sparse sets provide a rich setting for additive number theory, and in this paper we study various questions relating to the appearance of arithmetic progressions in these sets. In particular, for all $b$ we determine exactly the maximal length of an arithmetic progression that omits a base-$b$ digit." @default.
- W2892095864 created "2018-09-27" @default.
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- W2892095864 date "2018-09-07" @default.
- W2892095864 modified "2023-09-23" @default.
- W2892095864 title "Arithmetic Progressions with Restricted Digits" @default.
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