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A332866 Length of shortest ternary squarefree word having n periods. 1
1, 3, 7, 23, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A word is squarefree if it has no contiguous block inside it of the form xx, for a word x.

A period of a word w is an integer 1 <= p <= |w| such that w[i]=w[i+p] for all indices i that make sense.   For example, "alfalfa" has period 3.   Every nonempty word trivially has a period equal to its length.

LINKS

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

Daniel Gabric, Narad Rampersad, and Jeffrey Shallit, An inequality for the number of periods in a word, arXiv:2005.11718 [cs.DM], 2020.

EXAMPLE

Here is a brief table of the lexicographically least words of each length:

n=1:  0

n=2: 010

n=3: 0102010

n=4: 01021201021012010212010

n=5: 01021201020121020102120102012021020102120102012102010212010.

CROSSREFS

Sequence in context: A293466 A231722 A168612 * A127178 A001275 A058757

Adjacent sequences:  A332863 A332864 A332865 * A332867 A332868 A332869

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, May 11 2020

STATUS

approved

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Last modified June 20 09:40 EDT 2021. Contains 345162 sequences. (Running on oeis4.)