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
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
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, May 23 2020
STATUS
approved