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A342827 Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference d in the Thue-Morse sequence (A010060). 5
1, 2, 45, 4, 43, 90, 7, 8, 183, 86, 12, 180, 27, 14, 753, 16, 751, 366, 20, 172, 370, 24, 166, 360, 37, 54, 48, 28, 35, 1506, 31, 32, 3039, 1502, 36, 732, 94, 40, 205, 344, 56, 740, 725, 48, 663, 332, 326, 720, 321, 74, 137, 108, 60, 96, 617, 56, 378, 70, 101 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Ibai Aedo, Uwe Grimm, Yasushi Nagai, and Petra Staynova, On long arithmetic progressions in binary Morse-like words, arXiv:2101.02056 [math.CO], 2021.
Olga Parshina, On arithmetic index in the generalized Thue-Morse word, arXiv:1811.03884 [math.CO], 2018.
EXAMPLE
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.
CROSSREFS
Cf. A010060. The length of the longest monochromatic arithmetic progression is given by A342818.
Sequence in context: A161745 A048566 A321058 * A264438 A241762 A343424
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Mar 23 2021
STATUS
approved

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Last modified May 23 16:36 EDT 2024. Contains 372765 sequences. (Running on oeis4.)