Article (Scientific journals)
On digital sequences associated with Pascal's triangle
Mathonet, Pierre; Rigo, Michel; Stipulanti, Manon et al.
2022In Aequationes Mathematicae
Peer Reviewed verified by ORBi
 

Files


Full Text
arxiv.pdf
Author preprint (1.45 MB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
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
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Géométrie différentielle
Rigo, Michel  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Stipulanti, Manon  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Zenaïdi, Naïm ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Language :
English
Title :
On digital sequences associated with Pascal's triangle
Publication date :
15 December 2022
Journal title :
Aequationes Mathematicae
ISSN :
0001-9054
eISSN :
1420-8903
Publisher :
Birkhauser Verlag, Switzerland
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 18 January 2022

Statistics


Number of views
121 (12 by ULiège)
Number of downloads
115 (2 by ULiège)

Scopus citations®
 
1
Scopus citations®
without self-citations
1
OpenCitations
 
0

Bibliography


Similar publications



Contact ORBi