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arXiv · 1404.5237

Gaps in sumsets of $s$ pseudo s-th power sequences

Javier Cilleruelo·Jean-Marc Deshouillers
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Abstract

We study the length of the gaps between consecutive members in the sumset sA when A is a pseudo s-th power sequence, with s>1. We show that, almost surely, limsup (b_{n+1}-b_{n})/log (b_n) = s^s s!/Γ^s(1/s), where b_n are the elements of sA.

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Javier Cilleruelo, Jean-Marc Deshouillers. 2014-05-06. Gaps in sumsets of $s$ pseudo s-th power sequences. https://arxiv.org/abs/1404.5237

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