Self-Matching Properties of Beatty Sequences

الأصل · EN

We study the selfmatching properties of Beatty sequences, in particular of the graph of the function jβ against j for every quadratic unit β∈(0,1). We show that translation in the argument by an element Gᵢ of generalized Fibonacci sequence causes almost always the translation of the value of function by Gᵢ₋₁. More precisely, for fixed i∈, we have β(j+Gᵢ) = βj +Gᵢ₋₁, where j∉ Uᵢ. We determine the set Uᵢ of mismatches and show that it has a low frequency, namely βⁱ.