Gaps in sumsets of pseudo s-th power sequences
arXiv:1404.5237
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.
Corrected a mistake in Lemma 1