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 Chebyshevskii Sb., 2016, Volume 17, Issue 3, Pages 191–196 (Mi cheb507)

On transformations of periodic sequences

V. G. Chirskii

Moscow State Pedagogical University

Abstract: One of essential problems in generating pseudo-random numbers is the problem of periodicity of the resulting numbers. Some generators output periodic sequences. To avoid it several ways are used.
Here we present the following approach: supposed we have some order in the considered set. Let's invent some algorithm which produces disorder in the set. E.g. if we have a periodic sequence of integers, let's construct an irrational number implying the given set. Then the figures of the resulting number form a non-periodic sequence.
Here we can use continued fractions and Lagrange's theorem asserts that the resulting number is irrational.
Another approach is to use series of the form $\sum_{n=0}^\infty \frac{a_n}{n!}$ with a periodic sequence of integers $\{a_n\}, a_{n+T}=a_n$ which is irrational.
Here we consider polyadic series $\sum_{n=0}^\infty a_n n!$ with a periodic sequence of positive integers $\{a_n\},a_{n+T} = a_n$ and describe some of their properties.
Bibliography: 15 titles.

Keywords: periodic sequences, polyadic integers.

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Document Type: Article
UDC: 511.36
Accepted:12.09.2016

Citation: V. G. Chirskii, “On transformations of periodic sequences”, Chebyshevskii Sb., 17:3 (2016), 191–196

Citation in format AMSBIB
\Bibitem{Chi16} \by V.~G.~Chirskii \paper On transformations of periodic sequences \jour Chebyshevskii Sb. \yr 2016 \vol 17 \issue 3 \pages 191--196 \mathnet{http://mi.mathnet.ru/cheb507} \elib{http://elibrary.ru/item.asp?id=27452092}