A217235 -id:A217235 - cp's OEIS frontend

A171081 Van der Waerden numbers w(3, n).

9, 18, 22, 32, 46, 58, 77, 97, 114, 135, 160, 186, 218, 238, 279, 312, 349

Offset: 3

N. J. A. Sloane, based on an email from Tanbir Ahmed, Sep 07 2010

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

Knuth, Donald E., Satisfiability, Fascicle 6, volume 4 of The Art of Computer Programming. Addison-Wesley, 2015, page 5.

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.

Cf. A005346 (w(2, n)), A171082, A217235.

a(19) from Ahmed et al. - Jonathan Vos Post, Mar 01 2011

A171082 Van der Waerden numbers w(2;4,n).

Original entry on oeis.org

35, 55, 73, 109, 146, 309

Offset: 4

N. J. A. Sloane, based on an email from Tanbir Ahmed, Sep 07 2010 and Feb 22 2012

Tanbir Ahmed, Van der Waerden numbers
Tanbir Ahmed, On computation of exact van der Waerden numbers, Integers: Electronic Journal of Combinatorial Number Theory, 11 (2011), A71.

Cf. A005346, A171081, A217235.

cp's OEIS Frontend

A171081 Van der Waerden numbers w(3, n).

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