On a question of Mendès France on normal numbers

Authors: Verónica Becher, Manfred G. Madritsch.

Abstract: In 2008 or earlier, Michel Mendès France asked for an instance of a real number $x$ such that both $x$ and $1/x$ are simply normal to a given integer base $b$. We give a positive answer to this question by constructing a number $x$ such that both $x$ and its reciprocal $1/x$ are continued fraction normal as well as normal to all integer bases greater than or equal to $2$. Moreover, $x$ and $1/x$ are both computable.

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2022-05-27T13:19:43-03:00 27/mayo/2022|Papers|
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