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A274543
Smallest number m such that every binary string of length >= m contains either an n-th power or n-th antipower.
0
1, 2, 9, 24, 55
OFFSET
1,2
COMMENTS
By "n-th power" we mean n consecutive repetitions of a nonempty block. By "n-th antipower" we mean n consecutive blocks of the same size, no two of which are equal.
LINKS
Amanda Burcroff, (k,lambda)-Anti-Powers and Other Patterns in Words, arXiv:1807.07945 [math.CO], 2018.
G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Anti-powers in infinite words, arxiv preprint, 1606.02868 [cs.DM], 2016-2018.
EXAMPLE
For n = 3 the string of length 8 corresponding to 00101001 has no 3-power, nor 3-antipower. But every binary string of length 9 does.
CROSSREFS
Sequence in context: A259969 A023662 A131357 * A356114 A079997 A351252
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Jun 27 2016
STATUS
approved