A292773 - OEIS

%I #24 Oct 04 2021 10:23:51

%S 5,9,19,41,91,225

%N 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.

%H Y. Edel, C. Elsholtz, A. Geroldinger, S. Kubertin and L. Rackham, <a href="https://imsc.uni-graz.at/geroldinger/56-zero-sum-caps.pdf">Zero-sum problems in finite abelian groups and affine caps</a>, Quarterly Journal of Mathematics 58 (2), 159-186.

%H Christian Elsholtz, <a href="https://www.math.tugraz.at/~elsholtz/WWW/papers/papers08harborth.pdf">Lower bounds for multidimensional zero sums</a>, Combinatorica 24.3 (2004): 351-358.

%H H. Harborth, <a href="https://eudml.org/doc/151373">Ein Extremalproblem für Gitterpunkte</a>, J. Reine Angew. Math. 262 (1973), 356-360.

%H Aaron Potechin, <a href="https://doi.org/10.1007/s10623-007-9132-z">Maximal caps in AG (6, 3)</a>, Designs, Codes and Cryptography volume 46, pages 243-259 (2008).

%F a(n) = 2*A090245(n) + 1, (follows from Harborth, Hilfssatz 3). - _C. Elsholtz_, Oct 04 2021

%Y Cf. A090245.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Sep 30 2017

%E a(6), based on Potechin's paper, added by _C. Elsholtz_, Oct 04 2021