

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
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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 sumset and the productset for set sizes 40, 80, ..., 1000.


REFERENCES

Richard K. Guy, Unsolved Problems in Number Theory, 3rd ed., SpringerVerlag 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. 213218. DOI:10.1007/9783034854382_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



