A274543 - OEIS

A274543

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

1, 2, 9, 24, 55

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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

Table of n, a(n) for n=1..5.

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

Adjacent sequences: A274540 A274541 A274542 * A274544 A274545 A274546

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Jun 27 2016

STATUS

approved