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А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 27, 2017 10:35–11:05, Moscow, Department of Mechanics and Mathematics, Lomonosov Moscow State University
 


Finite sufficiently non-periodic sequences

V. G. Chirskiiabc

a Lomonosov Moscow State University
b Moscow State Pedagogical University
c The Academy of National Economy under the Government of the Russian Federation
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V. G. Chirskii


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Abstract: The paper [1] presents an approach to the transformation of a periodic sequence of digits $(a_{n+T} = a_{n})$ to a non-periodic one. In [1] and [2] we studied some arithmetic properties of certain series with periodic coefficients $a_{n}$.
For practical purposes, we can take only finitely many digits of the infinite expansion so here we propose a way to measure the periodicity of a finite sequence. We also introduce the notion of a finite sufficiently non-periodic sequence and try to link it with the arithmetic properties of the considered numbers.
[1] V.G. Chirskii, A.Yu. Nesterenko, An approach to the transformation of periodic sequences. Discrete Math. Appl. 27:1 (2017). P. 1 – 6.
[2] V.G. Chirskii, Arithmetic properties of polyadic series with periodic coefficients. Doklady Math. 90:3 (2014). P. 766 – 768.

Language: English

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