| 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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