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On ErdH{o}s and S\'ark\"ozy's sequences with Property P
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On ErdH{o}s and S\'ark\"ozy's sequences with Property P
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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 Erd\H{o}s and S\'ark\"ozy with a lower bound on the counting function of order $\frac{\sqrt{x}}{\log x}$.
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Cited by 2 Pith papers
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An LLM-based agent with Lean verification autonomously solved multiple open Erdős problems and OEIS conjectures in the first large-scale test.
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