We study the selfmatching properties of Beatty sequences, in particular of the graph of the function [Jβ] J against j for every quadratic unit β∈ (0,1). We show that translation in the argument by an element G; of a generalized Fibonacci sequence almost always causes the translation of the value of the function by G_(i-1)j_j. More precisely, for fixed i∈N, we have [β(j + G_i)] = [βj] + G_(i-1), where j ∈U_i, We determine the set U_i of mismatches and show that it has a low frequency, namely β~i.
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