On a universal extraction procedure
type: Item
instance of: scholarly article
title: On a universal extraction procedure
zbMATH Open document ID: 0843.11014
author: Guy Barat
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 1996-08-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/231182
full work available at URL: jtnb7-2.html
review text: Let \(\theta: \mathbb{N}\to \mathbb{N}\) be a strictly increasing sequence of positive integers, set \(E= \theta (\mathbb{N})\) and let \(n= \sum_{k\geq 0} \varepsilon_k (n) \cdot d^k\) be given in \(d\)-ary digital expansion. Following \textit{P. Liardet} [Acta Arith. 55, 119-135 (1990; Zbl 0716.11038)]\ the author considers sequences of the type \(\sigma_E (n)= \sum_{k\geq 0} \varepsilon_{\theta (k)} (n) d^k\). Periodicity and quasi-periodicity properties are investigated. For instance, it is proved that \(u\circ \sigma_E\) is \(d\)-automatic provided that \(E\) is ultimately periodic and \(u\) is \(d\)-automatic. Furthermore \(\sigma_E\) is quasi-periodic if and only if \(\lim_{n\to \infty} (\theta (n+1)- \theta (n))= \infty\).
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 11A67
zbMATH DE Number: 858573
zbMATH Keywords: automatic sequence
zbMATH Keywords: periodicity
zbMATH Keywords: digital expansion
zbMATH Keywords: quasi-periodicity
reviewed by: Robert F. Tichy
MaRDI profile type: Publication
OpenAlex ID: W2328913998
cites work: Suites algébriques, automates et substitutions
cites work: Uniform tag sequences
cites work: Sur les nombres qui ont des propriétés additives et multiplicatives données
cites work: Q4767350
cites work: Some metric properties of subsequences
DOI: 10.5802/JTNB.150
description: scientific article; zbMATH DE number 858573