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On q-Ary Periodic Sequences

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Abstract

We consider the problem of estimating the possible number of periods and the length of the periodic part of an irrational number depending on its measure of irrationality β. We state that the expansion of the fractional part of an irrational number α cannot start with a nonperiodic part of length (1 − δ)N and cannot terminate with a periodic part of length δN, regardless of the numeral system.

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Authors and Affiliations

  1. Moscow State Pedagogical University, Moscow, Russia

    A. Kh. Munos Vaskes

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  1. A. Kh. Munos Vaskes
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Correspondence to A. Kh. Munos Vaskes.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.

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Vaskes, A.K.M. On q-Ary Periodic Sequences. J Math Sci 276, 384–386 (2023). https://doi.org/10.1007/s10958-023-06753-y

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  • DOI: https://doi.org/10.1007/s10958-023-06753-y

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