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A304681 Smallest odd positive integer t such that the prefix of length tn of the Thue-Morse sequence (A010060) is an n-antipower. 1

%I #9 May 17 2018 21:38:48

%S 1,1,5,5,5,5,11,11,11,11,11,11,11,11,13,13,13,13,13,13,13,13,13,13,13,

%T 13,25,25,29,29,29,29,35,35,35,35,39,47,47,47,47,47,47,47,47,47,47,49,

%U 49,49,49,49,49,49,49,57,57,57,57,57,57,57,57,57,61,61,61,61,61,61,61,61,61,91,91,95,95,95,95

%N Smallest odd positive integer t such that the prefix of length tn of the Thue-Morse sequence (A010060) is an n-antipower.

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

%D 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.

%H Colin Defant, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i1p32">Anti-Power Prefixes of the Thue-Morse Word</a>, Electronic J. Combinatorics 24 (1) (2017), Paper #P1.32.

%e For n = 3, the prefixes (0)(1)(1) and (011)(010)(011) are not 3-antipowers, but the prefix (01101)(00110)(01011) is.

%Y Cf. A010060, A304682.

%K nonn

%O 1,3

%A _Jeffrey Shallit_, May 16 2018

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Last modified April 25 11:39 EDT 2024. Contains 371969 sequences. (Running on oeis4.)