A304682 Largest odd positive integer t such that the prefix of length tn of the Thue-Morse sequence (A010060) is not an n-antipower.

3, 3, 3, 9, 9, 9, 15, 17, 17, 17, 17, 17, 17, 17, 27, 33, 33, 33, 41, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 63, 77, 77, 77, 77, 77, 77, 77, 77, 77, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 123, 153, 153, 153, 165, 165, 165, 175, 175, 185, 185, 185, 185

Offset

3,1

Comments

A word of length tn is an n-antipower if all n consecutive blocks of length t are distinct.

Links

Table of n, a(n) for n=3..77.

Colin Defant, Anti-Power Prefixes of the Thue-Morse Word, Electronic J. Combinatorics 24 (1) (2017), Paper #P1.32.

Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, Anti-powers in infinite words, arXiv:1606.02868 [cs.DM], 2016-2018.

Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, Anti-powers in infinite words, Journal of Combinatorial Theory, Series A 157 (2018), 109-119.

Crossrefs

Cf. A010060, A304681.

Sequence in context: A253358 A256566 A132171 * A217645 A127975 A060828

Adjacent sequences: A304679 A304680 A304681 * A304683 A304684 A304685

Keyword

nonn

Author

Jeffrey Shallit, May 16 2018

Status

approved