<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Defined by Borel, a real number is normal to an integer base <italic>b</italic> ≥ 2 if in its base-<italic>b</italic> expansion every block of digits occurs with the same limiting frequency as every other block of the same length. We consider the problem of <italic>insertion</italic> in constructed base-<italic>b</italic> normal expansions to obtain normality to base (<italic>b</italic> + 1).</p>
</abstract>

Defined by Borel, a real number is normal to an integer base b ≥ 2 if in its base-b expansion every block of digits occurs with the same limiting frequency as every other block of the same length. We consider the problem of insertion in constructed base-b normal expansions to obtain normality to base (b + 1).

Insertion in Constructed Normal Numbers

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Insertion in Constructed Normal Numbers"}

Defined by Borel, a real number is normal to an integer base b ≥ 2 if in its base-b expansion every block of digits occurs with the same limiting frequency as...

Insertion in Constructed Normal Numbers

Published Online: May 31, 2022

Page range: 55 - 76

Received: May 31, 2021

Accepted: Mar 03, 2022

DOI: https://doi.org/10.2478/udt-2022-0008

Keywords
normal numbers, de Bruijn sequences, combinatorics on words

© 2022 Verónica Becher, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Insertion in Constructed Normal Numbers

Published Online: May 31, 2022

Page range: 55 - 76

Received: May 31, 2021

Accepted: Mar 03, 2022

DOI: https://doi.org/10.2478/udt-2022-0008

Keywordsnormal numbers, de Bruijn sequences, combinatorics on words

© 2022 Verónica Becher, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
normal numbers, de Bruijn sequences, combinatorics on words