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arXiv · 1409.5220

Normal number constructions for Cantor series with slowly growing bases

Dylan Airey·Bill Mance·Joseph Vandehey
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Abstract

Let $Q=(q_n)_{n=1}^\infty$ be a sequence of bases with $q_i\ge 2$. In the case when the $q_i$ are slowly growing and satisfy some additional weak conditions, we provide a construction of a number whose $Q$-Cantor series expansion is both $Q$-normal and $Q$-distribution normal. Moreover, this construction will result in a computable number provided we have some additional conditions on the computability of $Q$, and from this construction we can provide computable constructions of numbers with atypical normality properties.

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Dylan Airey, Bill Mance, Joseph Vandehey. 2014-09-18. Normal number constructions for Cantor series with slowly growing bases. https://arxiv.org/abs/1409.5220

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