A332866 Length of shortest ternary squarefree word having n periods.

1, 3, 7, 23, 59

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