A342827 Starting position of the first occurrence of the longest monochromatic arithmetic progression of difference d in the Thue-Morse sequence (A010060).

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

Offset

1,2

Links

Ibai Aedo, Table of n, a(n) for n = 1..2048

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

Adjacent sequences: A342824 A342825 A342826 * A342828 A342829 A342830

Keyword

nonn

Author

Jeffrey Shallit, Mar 23 2021

Status

approved