This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382870 #5 Apr 07 2025 10:06:49
%S A382870 1,2,4,5,8,8,13,13,27,27,45,53,66,109,129,147,147,170,192,250,286,317
%N A382870 Minimum period of an optimum covering of the set of integers by translates of its subset with diameter no greater than n, maximized over such subsets.
%H A382870 Béla Bollobás, Svante Janson, and Oliver Riordan, <a href="https://doi.org/10.1002/rsa.20346">On covering by translates of a set</a>, Random Structures and Algorithms, 38 (2011), 33-67; arXiv:<a href="https://arxiv.org/abs/0910.3815">0910.3815</a> [math.CO], 2009-2010. See Table 1.
%e A382870 For n = 3, the set S = {0, 1, 3} (diameter 3) covers the set of integers Z when translated by ...0, 1, 5, 6, 10, 11... with primitive period 5. Periodic coverings of Z by translates of S with smaller period are possible (e.g. by taking the entire Z as the set of translations) but they have greater density of overlaps and thus are not optimal. A different set can have a different period of an optimal covering, e.g. {0, 3} has the minimum period of 2 achieved by translations by ...0, 2, 4..., but a(n) maximizes over the subsets of diameter n, and the maximum is attained by S, so a(3) = 5.
%K A382870 nonn,more
%O A382870 0,2
%A A382870 _Andrey Zabolotskiy_, Apr 07 2025