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- Title
On digital sequences associated with Pascal's triangle.
- Authors
Mathonet, Pierre; Rigo, Michel; Stipulanti, Manon; Zénaïdi, Naïm
- Abstract
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 built with trinomial coefficients.
- Subjects
ELECTRONIC encyclopedias; TRIANGLES; BINOMIAL coefficients; INTEGERS; GRAY codes; NUMBER systems
- Publication
Aequationes Mathematicae, 2023, Vol 97, Issue 2, p391
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-022-00932-z