Remarks on a conjecture on certain integer sequences

  title={Remarks on a conjecture on certain integer sequences},
  author={Shigeki Akiyama and Horst Brunotte and Attila Peth{\"o} and Wolfgang Steiner},
  journal={Periodica Mathematica Hungarica},
The periodicity of sequences of integers (an)n∈Z satisfying the inequalities 0 ≤ an−1 + λan + an+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. 
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