|
| |
|
|
A007783
|
|
Mixed Van der Waerden numbers w(n, 3; 2).
|
|
3
| |
|
|
3, 6, 9, 18, 22, 32, 46, 58, 77, 97, 114, 135, 160, 186, 218, 238, 279, 312, 349
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Comments from Donald Vestal (vestal(AT)mwsc.edu), May 31 2005: "This is the smallest number M such that if each integer 1, 2, ..., M is colored using one of two colors (say red and blue), then there must be an arithmetic progression of length 3 in one color (red) or an arithmetic progression of length n in the other color (blue). So the first term, w(1, 3; 2), is 3."
Extended computations via SAT-solving in Ahmed, Kullmann, Snevily, 2011.
|
|
|
REFERENCES
| M. D. Beeler and P. E. O'Neil, Some new Van der Waerden numbers, Discrete Math., 28 (1979), 135-146.
V. Chvatal, Some unknown Van der Waerden numbers, pp. 31-33 of R. K. Guy et al., editors, Combinatorial Structures and Their Applications (Proceedings Calgary Conference Jun 1969}), Gordon and Breach, NY, 1970.
Bruce M. Landman and Aaron Robertson, Ramsey Theory on the Integers, Amer. Math. Soc., 2004.
|
|
|
LINKS
| T. Ahmed and O. Kullmann and H. Snevily, On the van der Waerden numbers w(2;3,t)
|
|
|
CROSSREFS
| Cf. A002886 has the same definition but an incorrect first term.
Sequence in context: A127644 A161338 A047847 * A050625 A025614 A182751
Adjacent sequences: A007780 A007781 A007782 * A007784 A007785 A007786
|
|
|
KEYWORD
| nonn,hard
|
|
|
AUTHOR
| Matthew Klimesh (matthew(AT)engin.umich.edu)
|
|
|
EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com) Jun 01, 2005
More terms for n=16,17,18,19 by Oliver Kullmann, Oct 28 2011
|
| |
|
|
