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Characterization of the unique expansions \(1=\sum^{\infty}_{i=1}q^{-n_ i}\) and related problems. (English) Zbl 0721.11005
Given a nonintegral base \(1<q<2\), the authors characterize the expansions of 1 base \(q\) for which uniqueness holds. Estimates for the number of consecutive zero digits in the greedy expansion of 1 are also obtained. These results are related to the sequence of real numbers which has finite base \(q\) expansions. Some open problems are given at the end of the article.

MSC:
11A67 Other number representations
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References:
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