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

Normal number constructions for Cantor series with slowly growing bases