A005346 Van der Waerden numbers W(2,n).

1, 3, 9, 35, 178, 1132

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more

Comments

a(6) = W(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

• 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.

Extensions

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