A292773 a(n) is the least integer m such that any choice of m elements in (Z_3)^n contains a subset of size 3 whose sum is zero.

5, 9, 19, 41, 91, 225

Offset

1,1

Links

Table of n, a(n) for n=1..6.

Y. Edel, C. Elsholtz, A. Geroldinger, S. Kubertin and L. Rackham, Zero-sum problems in finite abelian groups and affine caps, Quarterly Journal of Mathematics 58 (2), 159-186.

Christian Elsholtz, Lower bounds for multidimensional zero sums, Combinatorica 24.3 (2004): 351-358.

H. Harborth, Ein Extremalproblem für Gitterpunkte, J. Reine Angew. Math. 262 (1973), 356-360.

Aaron Potechin, Maximal caps in AG (6, 3), Designs, Codes and Cryptography volume 46, pages 243-259 (2008).

Formula

a(n) = 2*A090245(n) + 1, (follows from Harborth, Hilfssatz 3). - C. Elsholtz, Oct 04 2021

Crossrefs

Cf. A090245.

Sequence in context: A060161 A282730 A082674 * A228338 A309731 A253951

Adjacent sequences: A292770 A292771 A292772 * A292774 A292775 A292776

Keyword

nonn,more

Author

N. J. A. Sloane, Sep 30 2017

Extensions

a(6), based on Potechin's paper, added by C. Elsholtz, Oct 04 2021

Status

approved