cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

9, 18, 22, 32, 46, 58, 77, 97, 114, 135, 160, 186, 218, 238, 279, 312, 349
Offset: 3

Views

Author

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

Keywords

Comments

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

References

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

Crossrefs

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

Extensions

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

A217235 Van der Waerden numbers w(3; 3, 3, n).

Original entry on oeis.org

27, 51, 80, 107
Offset: 3

Views

Author

Tanbir Ahmed, Sep 28 2012

Keywords

Examples

			w(3; 3, 3, 3)=27, w(3; 3, 3, 4) = 51, and so on...
		

References

  • V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

Crossrefs

A217037 Van der Waerden numbers w(2;5,n).

Original entry on oeis.org

178, 206, 260
Offset: 5

Views

Author

Tanbir Ahmed, Sep 24 2012

Keywords

Comments

w(2;5,5)=178 (Stevens and Shantaram, 1978),w(2;5,6)=206 (Kouril, 2006), and w(2;5,7)=260 (Ahmed).

Examples

			w(2;5,5)=178.
		

References

  • M. Kouril, A Backtracking Framework for Beowulf Clusters with an Extension to Multi-Cluster Computation and Sat Benchmark Problem Implementation, Ph. D. Thesis, University of Cincinnati, Engineering: Computer Science and Engineering, 2006.

Crossrefs

Showing 1-3 of 3 results.