

A335107


Least period of the lengthn prefix of the ThueMorse sequence A010060.


0



1, 2, 3, 3, 3, 5, 6, 6, 6, 6, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 20, 20, 20, 20, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 40, 40, 40, 40, 40, 40, 40, 40, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48
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OFFSET

1,2


COMMENTS

An integer p, 1 <= p <= n, of a lengthn word x is said to be a period if x[i]=x[i+p] for 1 <= i <= np.
We have
a(n) = 3*2^i for 3*2^i < n <= 5*2^i, i >= 0;
a(n) = 5*2^i for 5*2^i < n <= 6*2^i, i >= 0.


LINKS

Table of n, a(n) for n=1..68.
D. Gabric, N. Rampersad, and J. Shallit, An inequality for the number of periods in a word, arxiv preprint arXiv:2005.11718 [cs.DM], May 24 2020.


EXAMPLE

For n = 10, the first 10 symbols of the ThueMorse sequence are 0110100110, which has period 6.


CROSSREFS

Cf. A010060.
Sequence in context: A160573 A141418 A287771 * A130499 A020910 A029065
Adjacent sequences: A335104 A335105 A335106 * A335108 A335109 A335110


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, May 23 2020


STATUS

approved



