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%I #32 Aug 24 2022 14:42:41
%S 2,2,8,2,6,8,8,2,10,6,4,8,4,8,20,2,18,10,5,6,8,4,6,8,6,4,11,8,5,20,32,
%T 2,34,18,4,10,7,5,9,6,7,8,8,4,10,6,6,8,6,6,9,4,7,11,9,8,13,5,9,20,6,
%U 32,68,2,66,34,6,18,12,4,9,10,6,7,9,5,8,9,11,6
%N Length of the longest monochromatic arithmetic progressions of difference d in the Thue-Morse sequence (A010060).
%C a(n) is the largest l such that there exists k with t(k) = t(k+n) = t(k+2*n) = ... = t(k+(l-1)*n), where t(n) = A010060(n).
%H Ibai Aedo, <a href="/A342818/b342818.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 Ibai Aedo, Uwe Grimm, Yasushi Nagai, and Petra Staynova, <a href="https://doi.org/10.1016/j.tcs.2022.08.013">Monochromatic Arithmetic Progressions in Binary Thue-Morse-Like Words</a>, Theor. Comp. Sci. (2022).
%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 n = 3, we have t(45) = t(48) = t(51) = t(54) = t(57) = t(60) = t(63) = t(66), and no k and m>8 exist such that t(k) = t(k+3) = t(k+2*3) = ... = t(k+(m-1)*3). So a(3)=8.
%Y Cf. A010060. Starting position of the first occurrence of a monochromatic arithmetic progression of difference n and length a(n) is given by A342827.
%K nonn
%O 1,1
%A _Jeffrey Shallit_, Mar 22 2021