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A005346 Van der Waerden numbers W(2,n).
(Formerly M2819)
10
1, 3, 9, 35, 178, 1132 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Named after the Dutch mathematician Bartel Leendert van der Waerden (1903-1996). - Amiram Eldar, Jun 24 2021

REFERENCES

Jacob E. Goodman and Joseph 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).

LINKS

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

Paul Erdős and Ronald 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 and H. van Maaren, A new method to construct lower bounds for Van de Waerden Numbers, Elec. J. Combinat., Vol. 14, No. 1 (2007), #R6.

Michal Kouril and Jerome L. Paul, The van der Waerden Number W(2,6) Is 1132, Experimental Mathematics, Vol. 17, No. 1 (2008), pp. 53-61.

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

Wikipedia, Van der Waerden number.

CROSSREFS

Cf. A121894.

Sequence in context: A107894 A155858 A000834 * A129094 A059424 A002575

Adjacent sequences:  A005343 A005344 A005345 * A005347 A005348 A005349

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified May 16 05:00 EDT 2022. Contains 353690 sequences. (Running on oeis4.)