دورية أكاديمية
On digital sequences associated with Pascal's triangle
| العنوان: | On digital sequences associated with Pascal's triangle |
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| المؤلفون: | Mathonet, Pierre, Rigo, Michel, Stipulanti, Manon, Zenaïdi, Naïm |
| المصدر: | Aequationes Mathematicae (2022-12-15) |
| بيانات النشر: | Birkhauser Verlag, 2022. |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Combinatorics on words, Pascal's triangle, Sierpinski’s triangle, Constructible regular polygon, Fermat numbers, Regular sequences, Automatic sequences, Base-p expansions, Pascal’s pyramid, Binomial coefficients, Evil and odious numbers, Nim sum, Physical, chemical, mathematical & earth Sciences, Mathematics, Physique, chimie, mathématiques & sciences de la terre, Mathématiques |
| الوصف: | We consider the sequence of integers whose nth term has base-p expansion given by the nth row of Pascal's triangle modulo p (where p is a prime number). We first present and generalize well-known relations concerning this sequence. Then, with the great help of Sloane's On-Line Encyclopedia of Integer Sequences, we show that it appears naturally as a subsequence of a 2-regular sequence. Its study provides interesting relations and surprisingly involves odious and evil numbers, Nim-sum and even Gray codes. Furthermore, we examine similar sequences emerging from prime numbers involving alternating sum-of-digits modulo p. This note ends with a discussion about Pascal's pyramid involving trinomial coefficients. |
| نوع الوثيقة: | journal article http://purl.org/coar/resource_type/c_6501Test article peer reviewed |
| اللغة: | English |
| العلاقة: | urn:issn:0001-9054; urn:issn:1420-8903 |
| DOI: | 10.1007/s00010-022-00932-z |
| الوصول الحر: | https://orbi.uliege.be/handle/2268/267187Test |
| حقوق: | open access http://purl.org/coar/access_right/c_abf2Test info:eu-repo/semantics/openAccess |
| رقم الانضمام: | edsorb.267187 |
| قاعدة البيانات: | ORBi |
| DOI: | 10.1007/s00010-022-00932-z |
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