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A005346 Van der Waerden numbers W(2,n).
(Formerly M2819)
1, 3, 9, 35, 178, 1132 (list; graph; refs; listen; history; text; internal format)



Extension (2,6) found by researcher in SAT techniques. - Jonathan Braunhut (jonbraunhut(AT)gmail.com), Jul 29 2007


J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 159.

M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 49.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..6.

P. Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory: van der Waerden's Theorem and Related Topics, L'Enseignement Math., Geneva, 1979, p. 325.

P. R. Herwig, M. J. H. Heule, P. M. van Lambalgen, H. van Maaren, A new method to construct lower bounds for Van de Waerden Numbers, Elec. J. Combinat. 14 (1) (2007), #R6.

M. Kouril and Jerome L. Paul, The van der Waerden Number W(2,6) Is 1132, Experimental Mathematics, 17 (2008), 53-61.

Eric Weisstein's World of Mathematics, van der Waerden Number

Wikipedia, Van der Waerden number.


Cf. A121894.

Sequence in context: A107894 A155858 A000834 * A129094 A059424 A002575

Adjacent sequences:  A005343 A005344 A005345 * A005347 A005348 A005349




N. J. A. Sloane


a(6) from Jonathan Braunhut (jonbraunhut(AT)gmail.com), Jul 29 2007



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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)