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arXiv · 1609.07935

On Erdős and Sárközy's sequences with Property P

Christian Elsholtz·Stefan Planitzer
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Abstract

A sequence $A$ of positive integers having the property that no element $a_i \in A$ divides the sum $a_j+a_k$ of two larger elements is said to have `Property P'. We construct an infinite set $S\subset \mathbb{N}$ having Property P with counting function $S(x)\gg\frac{\sqrt{x}}{\sqrt{\log x}(\log\log x)^2(\log \log \log x)^2}$. This improves on an example given by Erdős and Sárközy with a lower bound on the counting function of order $\frac{\sqrt{x}}{\log x}$.

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Christian Elsholtz, Stefan Planitzer. 2016-09-26. On Erdős and Sárközy's sequences with Property P. https://doi.org/10.1007/s00605-016-0995-9

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