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%I #7 Jan 11 2022 12:33:25
%S 0,2,8,34,177,1131
%N Van der Waerden numbers: A005346(n) - 1.
%C 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.
%C Some authors prefer this version to A005346.
%e 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.
%Y Cf. A005346.
%K nonn,more
%O 1,2
%A _James Dow Allen_, Sep 01 2006
%E Term a(6) (using A005346) from _Joerg Arndt_, Jun 06 2016