A121894 Van der Waerden numbers: A005346(n) - 1.

0, 2, 8, 34, 177, 1131

Offset

1,2

Comments

The maximum length of a string of 0's and 1's with no n-length "decimated substring" being all 0's or all 1's. A decimated substring is defined to be any subset {x_a, x_(a+p), x_(a+2p), x_(a+3p), ...} for any appropriate a, p.

Some authors prefer this version to A005346.

Links

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

Example

a(3) = 8 because 00110011 is the maximal string for n=3: appending 1 gives ......111 and appending 0 gives 0...0...0. No other starting string improves on this.

Crossrefs

Cf. A005346.

Sequence in context: A030944 A030871 A030960 * A061370 A126328 A268558

Adjacent sequences: A121891 A121892 A121893 * A121895 A121896 A121897

Keyword

nonn,more

Author

James Dow Allen, Sep 01 2006

Extensions

Term a(6) (using A005346) from Joerg Arndt, Jun 06 2016

Status

approved