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

Author

Jeffrey Shallit, Mar 23 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

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.
• Gandhar Joshi and Dan Rust, Monochromatic arithmetic progressions in the Fibonacci word, arXiv:2501.05830 [math.DS], 2025. See p. 7.
• Olga Parshina, On arithmetic index in the generalized Thue-Morse word, arXiv:1811.03884 [math.CO], 2018.

Crossrefs

Cf. A010060, A342818.