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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. 2
1, 4, 7, 11, 15, 20, 26, 30, 36, 44, 49, 57, 64, 71, 80, 86, 96, 104, 112, 121, 131, 141, 150, 160, 169, 179, 190, 200, 212, 222, 235, 248, 260, 272, 283, 296, 307, 320, 335, 348, 360, 371 (list; graph; refs; listen; history; text; internal format)
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

Al Zimmermann's Programming Contests, Sums and Products, 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

Cf. A263995.

Sequence in context: A130252 A130254 A278114 * A172472 A134918 A310741

Adjacent sequences:  A263993 A263994 A263995 * A263997 A263998 A263999

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Nov 15 2015

STATUS

approved

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Last modified June 20 09:27 EDT 2019. Contains 324234 sequences. (Running on oeis4.)