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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.
Received: 30.06.2016 Accepted: 12.09.2016
Citation:
V. G. Chirskii, “On transformations of periodic sequences”, Chebyshevskii Sb., 17:3 (2016), 191–196
Linking options:
https://www.mathnet.ru/eng/cheb507 https://www.mathnet.ru/eng/cheb/v17/i3/p191
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Abstract page: | 237 | Full-text PDF : | 67 | References: | 35 |
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