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:
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arXiv e-prints
- Pub Date:
- August 2021
- DOI:
- 10.48550/arXiv.2108.06804
- arXiv:
- arXiv:2108.06804
- Bibcode:
- 2021arXiv210806804B
- Keywords:
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- Mathematics - Number Theory;
- 11K16;
- 11J70
- E-Print:
- 15 pages. arXiv admin note: text overlap with arXiv:1704.03622