

A330582


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


0




OFFSET

1,2


COMMENTS

A square is two consecutive identical blocks, such as "201201". An nantipower is n consecutive pairwise distinct blocks.
Here are the lexicographically least strings of length a(n)1 having neither a square nor an nantipower:
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, Antipowers in infinite words, arXiv:1606.02868 [cs.DM], 20162018.
Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, Antipowers in infinite words, Journal of Combinatorial Theory, Series A 157 (2018), 109119.


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



