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 A171081 Van der Waerden numbers w(3, n). 4
 9, 18, 22, 32, 46, 58, 77, 97, 114, 135, 160, 186, 218, 238, 279, 312, 349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS The two-color van der Waerden number w(3,n) is also denoted as w(2;3,n). Ahmed et al. give lower bounds for a(20)-a(30) which may in fact be the true values. - N. J. A. Sloane, May 13 2018 B. Green shows that w(3,n) is bounded below by n^b(n), where b(n) = c*(log(n)/ log(log(n)))^(1/3). T. Schoen proves that for large n one has w(3,n) < exp(n^(1 - c)) for some constant c > 0. - Peter Luschny, Feb 03 2021 REFERENCES Knuth, Donald E., Satisfiability,  Fascicle 6, volume 4 of The Art of Computer Programming. Addison-Wesley, 2015, page 5. LINKS Tanbir Ahmed, Oliver Kullmann, and Hunter Snevily, On the van der Waerden numbers w(2;3,t), arXiv:1102.5433 [math.CO], 2011-2014; Discrete Applied Math., 174 (2014), 27-51. Ben Green, New lower bounds for van der Waerden numbers, arXiv:2102.01543 [math.CO], Feb. 2021. Tomasz Schoen, A subexponential bound for van der Waerden numbers, arXiv:2006.02877 [math.CO], June 2020. CROSSREFS Cf. A005346 (w(2, n)), A171082, A217235. Sequence in context: A222623 A141469 A046412 * A232056 A109661 A015798 Adjacent sequences:  A171078 A171079 A171080 * A171082 A171083 A171084 KEYWORD nonn,hard,more AUTHOR N. J. A. Sloane, based on an email from Tanbir Ahmed, Sep 07 2010 EXTENSIONS a(19) from Ahmed et al. - Jonathan Vos Post, Mar 01 2011 STATUS approved

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