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A335107 Least period of the length-n prefix of the Thue-Morse 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

An integer p, 1 <= p <= n, of a length-n word x is said to be a period if x[i]=x[i+p] for 1 <= i <= n-p.

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 Thue-Morse 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

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Last modified June 18 04:41 EDT 2021. Contains 345098 sequences. (Running on oeis4.)