On a question of Mendès France on normal numbers
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.06804
 Bibcode:
 2021arXiv210806804B
 Keywords:

 Mathematics  Number Theory;
 11K16;
 11J70
 EPrint:
 15 pages. arXiv admin note: text overlap with arXiv:1704.03622