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Irregularities in the Distribution of Prime Numbers in a Beatty Sequence

Part of: Elementary number theory Sequences and sets

Published online by Cambridge University Press:  16 December 2019

Janyarak Tongsomporn  and
Jörn Steuding
Janyarak Tongsomporn
Affiliation:
Walailak University, School of Science, Nakhon Si Thammarat, 80 160, Thailand Email: [email protected]
Jörn Steuding
Affiliation:
Department of Mathematics, Würzburg University, Am Hubland, 97 218Würzburg, Germany Email: [email protected]
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Abstract

We prove irregularities in the distribution of prime numbers in any Beatty sequence ${\mathcal{B}}(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$, where $\unicode[STIX]{x1D6FC}$ is a positive real irrational number of finite type.

Keywords

prime numbersirregularitiesMaier’s matrix methodBeatty sequence

MSC classification

Primary: 11A41: Primes
Secondary: 11B83: Special sequences and polynomials
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 4 , December 2020 , pp. 738 - 743
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Copyright
© Canadian Mathematical Society 2019

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