Abstract
For each positive irrational number α, the Beatty sequence generated by α is given byB(α)=(⌊bα⌋)b≥1. Previously, Pongsriiam and his coauthors determined the structure of the sumsets B(α)+B(α), B(α2)+B(α2)+B(α2), B(α)+B(α2)+B(α2), B(α)+B(α2), and B(α2)+B(α2), where α=(1+5)/2 is the golden ratio. In this article, we extend the investigation to the sumsets B(x)+B(x), B(x)+B(y)+B(y), and B(y)+B(y)+B(y) where x and y are irrational numbers such that 1<x<y and 1/x+1/y=1. We also give connections to logic.
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