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A330582 a(n) is the least integer k such that every ternary string of length >= k contains either a square or an n-antipower. 0
1, 2, 4, 16, 26, 35, 54, 72, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A square is two consecutive identical blocks, such as "201201".  An n-antipower is n consecutive pairwise distinct blocks.

Here are the lexicographically least strings of length a(n)-1 having neither a square nor an n-antipower:

n = 3: 010

n = 4: 010201210201021

n = 5: 0102120102012102010212010

n = 6: 0102120102101201021201210201021012

n = 7: 01202120102012102120102101202120121021202101202120102

n = 8: 01020121012010210120212010201210120210201210120102101202102012101202102

n = 9: 01020121020102120210121020102120121020102101201021202101210212010210121020102120210120102120210

LINKS

Table of n, a(n) for n=1..9.

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

Sequence in context: A292369 A153665 A015775 * A104258 A143904 A144797

Adjacent sequences:  A330579 A330580 A330581 * A330583 A330584 A330585

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Dec 18 2019

STATUS

approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)