Geodesic
Normal number constructions for Cantor series with slowly growing bases
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 465-480
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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.
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.
DOI : 10.1007/s10587-016-0269-7
Classification : 11A63, 11K16
Keywords: Cantor series; normal number 
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Airey, Dylan; Mance, Bill; Vandehey, Joseph. Normal number constructions for Cantor series with slowly growing bases. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 2, pp. 465-480. doi: 10.1007/s10587-016-0269-7

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