OFFSET

0,2

COMMENTS

The density Hales-Jewett theorem implies that a(n) = o(3^n). a(n) is studied further in the polymath1 project, see link below.

LINKS

H. Furstenberg, Y. Katznelson, A density version of the Hales-Jewett theorem for k=3, Graph Theory and Combinatorics (Cambridge, 1988). Discr. Math. 75 (1989) no. 1-3, 227-241.

H. Furstenberg and Y. Katznelson, A density version of the Hales-Jewett theorem, J. Anal. Math. 57 (1991), 64-119.

K. O'Bryant, Sets of natural numbers with proscribed subsets, arXiv:1410.4900 [math.NT], 2014-2015.

K. O'Bryant, Sets of Natural Numbers with Proscribed Subsets, J. Int. Seq. 18 (2015) # 15.7.7

D. H. J. Polymath, Density Hales-Jewett and Moser numbers, arXiv:1002.0374 [math.CO]

Polymath1 Project, Wiki Main Page

EXAMPLE

For n=2, one example that shows a(2) is at least 6 is { 11, 13, 22, 23, 31, 32 }.

CROSSREFS

KEYWORD

hard,more,nonn,changed

AUTHOR

Terence Tao, Feb 20 2009

STATUS

approved