A330582 a(n) is the least integer k such that every ternary string of length >= k contains either a square or an n-antipower.

1, 2, 4, 16, 26, 35, 54, 72, 96

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: A357917 A153665 A015775 * A104258 A143904 A144797

Adjacent sequences: A330579 A330580 A330581 * A330583 A330584 A330585

Keyword

nonn,more

Author

Jeffrey Shallit, Dec 18 2019

Status

approved