A335107 - OEIS

%I #8 May 26 2020 06:03:57

%S 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,

%T 24,24,24,24,24,24,24,24,24,24,24,24,24,24,40,40,40,40,40,40,40,40,48,

%U 48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48

%N Least period of the length-n prefix of the Thue-Morse sequence A010060.

%C 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.

%C We have

%C a(n) = 3*2^i for 3*2^i < n <= 5*2^i, i >= 0;

%C a(n) = 5*2^i for 5*2^i < n <= 6*2^i, i >= 0.

%H D. Gabric, N. Rampersad, and J. Shallit, <a href="https://arxiv.org/abs/2005.11718">An inequality for the number of periods in a word</a>, arxiv preprint arXiv:2005.11718 [cs.DM], May 24 2020.

%e For n = 10, the first 10 symbols of the Thue-Morse sequence are 0110100110, which has period 6.

%Y Cf. A010060.

%K nonn

%O 1,2

%A _Jeffrey Shallit_, May 23 2020