OFFSET
1,1
COMMENTS
This is the smallest number M such that if each integer 1, 2, ..., M is colored using one of two colors (say red and blue), then there must be an arithmetic progression of length 3 in one color (red) or an arithmetic progression of length n in the other color (blue). So the first term, w(1, 3; 2), is 3. - Donald Vestal, May 31 2005
Extended computations via SAT-solving in Ahmed, Kullmann, Snevily, 2011.
REFERENCES
V. Chvatal, Some unknown Van der Waerden numbers, pp. 31-33 of R. K. Guy et al., editors, Combinatorial Structures and Their Applications (Proceedings Calgary Conference Jun 1969), Gordon and Breach, NY, 1970.
Bruce M. Landman and Aaron Robertson, Ramsey Theory on the Integers, Amer. Math. Soc., 2004.
LINKS
T. Ahmed and O. Kullmann and H. Snevily, On the van der Waerden numbers w(2;3,t), arXiv:1102.5433 [math.CO], 2011-2014.
M. D. Beeler and P. E. O'Neil, Some new Van der Waerden numbers, Discrete Math., 28 (1979), 135-146.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Matthew Klimesh (matthew(AT)engin.umich.edu)
EXTENSIONS
Entry revised by N. J. A. Sloane, Jun 01 2005
a(16)-a(19) from Oliver Kullmann, Oct 28 2011
STATUS
approved