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%I #22 Nov 09 2015 11:54:21
%S 3,6,9,18,22,32,46,58,77,97,114,135,160,186,218,238,279,312,349
%N Mixed Van der Waerden numbers w(n, 3; 2).
%C 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
%C Extended computations via SAT-solving in Ahmed, Kullmann, Snevily, 2011.
%D 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.
%D Bruce M. Landman and Aaron Robertson, Ramsey Theory on the Integers, Amer. Math. Soc., 2004.
%H T. Ahmed and O. Kullmann and H. Snevily, <a href="http://arxiv.org/abs/1102.5433">On the van der Waerden numbers w(2;3,t)</a>, arXiv:1102.5433 [math.CO], 2011-2014.
%H M. D. Beeler and P. E. O'Neil, <a href="http://dx.doi.org/10.1016/0012-365X(79)90090-6">Some new Van der Waerden numbers</a>, Discrete Math., 28 (1979), 135-146.
%Y Cf. A002886 has the same definition but an incorrect first term.
%K nonn,hard
%O 1,1
%A Matthew Klimesh (matthew(AT)engin.umich.edu)
%E Entry revised by _N. J. A. Sloane_, Jun 01 2005
%E a(16)-a(19) from _Oliver Kullmann_, Oct 28 2011
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