OFFSET
1,2
COMMENTS
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).
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer-Verlag New York, 2004. Problem F18.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 1..205
P. Erdős and E. Szemeredi, On sums and products of integers, Studies in Pure Mathematics, Birkhäuser, Basel, 1983, pp. 213-218. DOI:10.1007/978-3-0348-5438-2_19
Kevin Hartnett, How a Strange Grid Reveals Hidden Connections Between Simple Numbers, Quanta Magazine, Feb. 6 2019.
Al Zimmermann's Programming Contests, Sums and Products I, Nov 2015 - Feb 2016.
EXAMPLE
a(1) = 1 because for the set {2} the union of {2+2} and {2*2} = {4}.
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}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Nov 15 2015
STATUS
approved