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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

%I

%S 1,2,9,24,55

%N Smallest number m such that every binary string of length >= m contains either an n-th power or n-th antipower.

%C 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.

%H Amanda Burcroff, <a href="https://arxiv.org/abs/1807.07945">(k,lambda)-Anti-Powers and Other Patterns in Words</a>, arXiv:1807.07945 [math.CO], 2018.

%H G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, <a href="http://arxiv.org/abs/1606.02868">Anti-powers in infinite words</a>, arxiv preprint, 1606.02868 [cs.DM], 2016-2018.

%e 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.

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Jun 27 2016

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)