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Автор Cassaigne, Julien
Автор Finch, Steven R.
Дата выпуска 1995
dc.description For odd v ≥ 5, Schmerl and Spiegel have proved that the 1-additive sequence (2, v) has precisely two even terms and, consequently, is regular. For 5 ≤ v ≡ 1 mod 4, we prove, using a different approach, that the 1-additive sequence (4, v) has precisely three even terms. The proof draws upon the periodicity properties of a certain ternary quadratic recurrence.Unlike the case of (2, v), the regularity of (4, v) can be captured by expressions in closed form. For example, its period can be written as an exponential sum of binary digit sums. Therefore the asymptotic density δ(v) of (4, v) tends to 0 as v → ∞, but is misbehaved in the sense thatThis is proved using techniques adapted from Harborth and Stolarsky.
Формат application.pdf
Издатель Taylor & Francis Group
Копирайт Copyright Taylor and Francis Group, LLC
Название A Class of 1-Additive Sequences and Quadratic Recurrences
Тип research-article
DOI 10.1080/10586458.1995.10504307
Electronic ISSN 1944-950X
Print ISSN 1058-6458
Журнал Experimental Mathematics
Том 4
Первая страница 49
Последняя страница 60
Аффилиация Cassaigne, Julien; LITP, Institut Blaise Pascal
Аффилиация Finch, Steven R.; <sup>b</sup> 6 Foster Street, Wakefield, MA, 01880, USA E-mail: sfinch@gnu.aLmit.edu
Выпуск 1
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