A342827 - OEIS

A342827

Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference d in the Thue-Morse sequence (A010060).

%I #18 Jun 18 2024 23:32:25

%S 1,2,45,4,43,90,7,8,183,86,12,180,27,14,753,16,751,366,20,172,370,24,

%T 166,360,37,54,48,28,35,1506,31,32,3039,1502,36,732,94,40,205,344,56,

%U 740,725,48,663,332,326,720,321,74,137,108,60,96,617,56,378,70,101

%N Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference d in the Thue-Morse sequence (A010060).

%C The length of this longest progression is A342818(n).

%H Ibai Aedo, <a href="/A342827/b342827.txt">Table of n, a(n) for n = 1..2048</a>

%H Ibai Aedo, Uwe Grimm, Yasushi Nagai, and Petra Staynova, <a href="https://arxiv.org/abs/2101.02056">On long arithmetic progressions in binary Morse-like words</a>, arXiv:2101.02056 [math.CO], 2021.

%H Olga Parshina, <a href="https://arxiv.org/abs/1811.03884">On arithmetic index in the generalized Thue-Morse word</a>, arXiv:1811.03884 [math.CO], 2018.

%e For example, the smallest i with t(i)=t(i+3)=t(i+6)=t(i+9)=t(i+12)=t(i+15)=t(i+18)=t(i+21) is i=45 and so, a(3)=45.

%Y Cf. A010060, A342818.

%K nonn

%O 1,2

%A _Jeffrey Shallit_, Mar 23 2021