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A171081
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Van der Waerden numbers w(3, n).
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4
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9, 18, 22, 32, 46, 58, 77, 97, 114, 135, 160, 186, 218, 238, 279, 312, 349
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OFFSET
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3,1
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COMMENTS
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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
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REFERENCES
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Knuth, Donald E., Satisfiability, Fascicle 6, volume 4 of The Art of Computer Programming. Addison-Wesley, 2015, page 5.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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