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math.NT2023
Decomposition of Beatty and Complementary Sequences
Geremias Polanco
In this paper we express the difference of two complementary Beatty sequences, as the sum of two Beatty sequences closely related to them. In the process we introduce a new Algorit…
math.NT2017★ 1 cited
A variation on the theme of Nicomachus
Florian Luca, Geremías Polanco, Wadim Zudilin
We prove some conjectures of K. Stolarsky concerning the first and third moment of the Beatty sequences with the golden section and its square.
math.NT2015★ 2 cited
Continuous Distribution Arising From the Three Gaps Theorem
Geremías Polanco, Daniel Schultz, Alexandru Zaharescu
The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts . It is known that if one averages over α, the dis…