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 A263996 #41 Apr 25 2023 08:07:16
%S A263996 1,4,7,11,15,20,26,30,36,44,49,57,64,71,80,86,96,104,112,121,131,141,
%T A263996 150,160,169,179,190,200,212,222,235,248,260,272,283,296,307,320,335,
%U A263996 348,360,371
%N A263996 Smallest possible cardinality of the union of the set of pairwise sums and the set of pairwise products from a set of n positive integers.
%C A263996 The November 2015 - February 2016 round of Al Zimmermann's programming contests asked for optimal sets producing a(40), a(80), a(120), ..., a(1000).
%D A263996 Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer-Verlag New York, 2004. Problem F18.
%H A263996 Hugo Pfoertner, <a href="/A263996/b263996.txt">Table of n, a(n) for n = 1..205</a>
%H A263996 P. Erdős and E. Szemeredi, <a href="http://renyi.hu/~p_erdos/1983-18.pdf">On sums and products of integers</a>, Studies in Pure Mathematics, Birkhäuser, Basel, 1983, pp. 213-218. DOI:10.1007/978-3-0348-5438-2_19
%H A263996 Kevin Hartnett, <a href="https://www.quantamagazine.org/the-sum-product-problem-shows-how-addition-and-multiplication-constrain-each-other-20190206/">How a Strange Grid Reveals Hidden Connections Between Simple Numbers</a>, Quanta Magazine, Feb. 6 2019.
%H A263996 Al Zimmermann's Programming Contests, <a href="http://azspcs.com/Contest/SumsAndProducts1">Sums and Products I</a>, Nov 2015 - Feb 2016.
%e A263996 a(1) = 1 because for the set {2} the union of {2+2} and {2*2} = {4}.
%e A263996 a(7) = 26: The set {1,2,3,4,6,8,12} has the set of pairwise sums {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,24} and the set of pairwise products {1,2,3,4,6,8,9,12,16,18,24,32,36,48,64,72,96,144}. The cardinality of the union of the two sets, {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,24,32,36,48,64,72,96,144}, is 26. This is the first nontrivial case with a(n) < A263995(n), which uses the set {1..n}.
%Y A263996 Cf. A027424, A263995.
%K A263996 nonn
%O A263996 1,2
%A A263996 _Hugo Pfoertner_, Nov 15 2015