<abstract xmlns="http://www.w3.org/1999/xhtml"> Given a real number 0.a1a2a3 . . . that is normal to base b, we examine increasing sequences ni so that the number 0.an1an2an3 . . . are normal to base b. Classically, it is known that if the ni form an arithmetic progression, then this will work. We give several more constructions including ni that are recursively defined based on the digits ai. Of particular interest, we show that if a number is normal to base b, then removing all the digits from its expansion which equal (b−1) leaves a base-(b−1) expansion that is normal to base (b − 1)</abstract>

Given a real number 0.a1a2a3 . . . that is normal to base b, we examine increasing sequences ni so that the number 0.an1an2an3 . . . are normal to base b. Classically, it is known that if the ni form an arithmetic progression, then this will work. We give several more constructions including ni that are recursively defined based on the digits ai. Of particular interest, we show that if a number is normal to base b, then removing all the digits from its expansion which equal (b−1) leaves a base-(b−1) expansion that is normal to base (b − 1)

Uncanny Subsequence Selections That Generate Normal Numbers

Uniform distribution theory

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

{"article-title":"Uncanny Subsequence Selections That Generate Normal Numbers"}

Given a real number 0.a1a2a3 . . . that is normal to base b, we examine increasing sequences ni so that the number 0.an1an2an3 . . . are normal to base b....

Uncanny Subsequence Selections That Generate Normal Numbers

Publié en ligne: 30 janv. 2018

Pages: 65 - 75

Reçu: 04 août 2016

Accepté: 10 janv. 2017

DOI: https://doi.org/10.1515/udt-2017-0015

Mots clés
normal numbers

© 2018

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

Uncanny Subsequence Selections That Generate Normal Numbers

Publié en ligne: 30 janv. 2018

Pages: 65 - 75

Reçu: 04 août 2016

Accepté: 10 janv. 2017

DOI: https://doi.org/10.1515/udt-2017-0015

Mots clésnormal numbers

© 2018

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

Mots clés
normal numbers