1,1

Comments from Donald Vestal (vestal(AT)mwsc.edu), May 31 2005: "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."

M. D. Beeler and P. E. O'Neil, Some new Van der Waerden numbers, Discrete Math., 28 (1979), 135-146.

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.

A002886 has the same definition but an incorrect first term.

Sequence in context: A127644 A161338 A047847 this_sequence A050625 A025614 A057576

Adjacent sequences: A007780 A007781 A007782 this_sequence A007784 A007785 A007786

nonn,hard

Matthew Klimesh (matthew(AT)engin.umich.edu)

Entry revised by N. J. A. Sloane (njas(AT)research.att.com) Jun 01, 2005