FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On numbers with fixed last digits of linear recurrent base expansion |
Shutov A.V. |
2024, issue 1, P. 141-150 DOI: https://doi.org/10.47910/FEMJ202413 |
Abstract |
| We study some properties of natural numbers with fixed last digits of linear recurrent base expansion. Using the theory of Rauzy fractals we describe possible densities of such numbers and possible first differences between them. |
Keywords: linear recurrent base expansion, last digits, densities, first differences, Rauzy fractals. |
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References |
| [1] Berthe V., Siegel A., “Tilings associated with beta-numeration and substitution”, Integers: electronic journal of combinatorial number theory, 5, (2008), A02. [2] Frougny C., Solomyak B., “Finite beta-expansions”, Ergodic Theory and Dynamical Systems, 12:4, (1992), 713–723. [3] Akiyama S., “Pisot number system and its dual tiling”, Physics and Theoretical Computer Science, IOS Press, 2007, 133–154. [4] Berthe V., Siegel A., “Tilings associated with beta-numeration and substitution”, Integers: electronic journal of combinatorial number theory, 5, (2008), A02. [5] Shutov A.V., “Obobshchennye razbieniia Rozi i mnozhestva ogranichennogo ostatka”, Chebyshevskii sbornik, 20:3, (2019), 372–389. [6] Shutov A.V., “Obobshchennye razbieniia Rozi i lineinye rekurrentnye posledovatel'nosti”, Chebyshevskii sbornik, 22:2, (2021), 313–333. [7] Shutov A.V., “Trigonometricheskie summy nad odnomernymi kvazireshetkami proizvol'noi korazmernosti”, Matematicheskie zametki, 97:5, (2015), 781–793. |