Remarks on a conjecture on certain integer sequences

Shigeki Akiyama, Horst Brunotte, A. Pethő, Wolfgang Steiner

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The periodicity of sequences of integers (a n)n∈ℤ satisfying the inequalities 0 ≤ a n-1 + λa n + a n+1 <1 (n ∈ ℤ) is studied for real λ with |λ| <2. Periodicity is proved in case λ is the golden ratio; for other values of λ statements on possible period lengths are given. Further interesting results on the morphology of periods are illustrated. The problem is connected to the investigation of shift radix systems and of Salem numbers.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalPeriodica Mathematica Hungarica
Volume52
Issue number1
DOIs
Publication statusPublished - Mar 2006

Fingerprint

Integer Sequences
Periodicity
Salem numbers
Golden ratio
Integer

Keywords

  • Integer sequences
  • Periodicity

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Remarks on a conjecture on certain integer sequences. / Akiyama, Shigeki; Brunotte, Horst; Pethő, A.; Steiner, Wolfgang.

In: Periodica Mathematica Hungarica, Vol. 52, No. 1, 03.2006, p. 1-17.

Research output: Contribution to journalArticle

Akiyama, Shigeki ; Brunotte, Horst ; Pethő, A. ; Steiner, Wolfgang. / Remarks on a conjecture on certain integer sequences. In: Periodica Mathematica Hungarica. 2006 ; Vol. 52, No. 1. pp. 1-17.
@article{21fd0a040c1f4ee3ac26065e91ccb419,
title = "Remarks on a conjecture on certain integer sequences",
abstract = "The periodicity of sequences of integers (a n)n∈ℤ satisfying the inequalities 0 ≤ a n-1 + λa n + a n+1 <1 (n ∈ ℤ) is studied for real λ with |λ| <2. Periodicity is proved in case λ is the golden ratio; for other values of λ statements on possible period lengths are given. Further interesting results on the morphology of periods are illustrated. The problem is connected to the investigation of shift radix systems and of Salem numbers.",
keywords = "Integer sequences, Periodicity",
author = "Shigeki Akiyama and Horst Brunotte and A. Pethő and Wolfgang Steiner",
year = "2006",
month = "3",
doi = "10.1007/s10998-006-0002-7",
language = "English",
volume = "52",
pages = "1--17",
journal = "Periodica Mathematica Hungarica",
issn = "0031-5303",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - Remarks on a conjecture on certain integer sequences

AU - Akiyama, Shigeki

AU - Brunotte, Horst

AU - Pethő, A.

AU - Steiner, Wolfgang

PY - 2006/3

Y1 - 2006/3

N2 - The periodicity of sequences of integers (a n)n∈ℤ satisfying the inequalities 0 ≤ a n-1 + λa n + a n+1 <1 (n ∈ ℤ) is studied for real λ with |λ| <2. Periodicity is proved in case λ is the golden ratio; for other values of λ statements on possible period lengths are given. Further interesting results on the morphology of periods are illustrated. The problem is connected to the investigation of shift radix systems and of Salem numbers.

AB - The periodicity of sequences of integers (a n)n∈ℤ satisfying the inequalities 0 ≤ a n-1 + λa n + a n+1 <1 (n ∈ ℤ) is studied for real λ with |λ| <2. Periodicity is proved in case λ is the golden ratio; for other values of λ statements on possible period lengths are given. Further interesting results on the morphology of periods are illustrated. The problem is connected to the investigation of shift radix systems and of Salem numbers.

KW - Integer sequences

KW - Periodicity

UR - http://www.scopus.com/inward/record.url?scp=33645313743&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645313743&partnerID=8YFLogxK

U2 - 10.1007/s10998-006-0002-7

DO - 10.1007/s10998-006-0002-7

M3 - Article

VL - 52

SP - 1

EP - 17

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

SN - 0031-5303

IS - 1

ER -