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A263995 Cardinality of the union of the set of sums and the set of products made from pairs of integers from {1...n}. 2
2, 4, 7, 11, 15, 20, 27, 32, 39, 46, 56, 63, 75, 83, 93, 102, 118, 127, 146, 156, 169, 182, 204, 215, 231, 245, 261, 274, 302, 315, 346, 361, 379, 398, 418, 432, 469, 489, 510, 527, 567, 585, 627, 647, 669, 693, 739, 756, 788, 810, 838, 862, 914, 937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The November 2015 - Feb 2016 round of Al Zimmermann's Programming Contests asks for sets of positive integers (instead of {1...n}) minimizing the cardinality of the union of the sum-set and the product-set for set sizes 40, 80, ..., 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..10000

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(3)=7 because the union of the set of sums {1+1, 1+2, 1+3, 2+2, 2+3, 3+3) and the set of products {1*1, 1*2, 1*3, 2*2, 2*3, 3*3} = {2,3,4,5,6} U {1,2,3,4,6,9} = {1,2,3,4,5,6,9} has cardinality 7.

CROSSREFS

Cf. A263996.

Sequence in context: A025696 A077169 A094277 * A293239 A261878 A261993

Adjacent sequences:  A263992 A263993 A263994 * A263996 A263997 A263998

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Nov 15 2015

EXTENSIONS

Comment describing goal of Al Zimmermann's Programming Contest corrected by Al Zimmermann, Nov 24 2015

STATUS

approved

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Last modified June 25 18:30 EDT 2019. Contains 324353 sequences. (Running on oeis4.)