Remarks on a conjecture on certain integer sequences

Shigeki Akiyama, Horst Brunotte, Attila Pethő, Wolfgang Steiner

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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
Issue number1
Publication statusPublished - Mar 2006



  • Integer sequences
  • Periodicity

ASJC Scopus subject areas

  • Mathematics(all)

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