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a(n) is the least integer k such that every ternary string of length >= k contains either a square or an n-antipower.
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%I #6 Dec 18 2019 17:23:45

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

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

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

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

%C n = 3: 010

%C n = 4: 010201210201021

%C n = 5: 0102120102012102010212010

%C n = 6: 0102120102101201021201210201021012

%C n = 7: 01202120102012102120102101202120121021202101202120102

%C n = 8: 01020121012010210120212010201210120210201210120102101202102012101202102

%C n = 9: 01020121020102120210121020102120121020102101201021202101210212010210121020102120210120102120210

%H Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, <a href="https://arxiv.org/abs/1606.02868">Anti-powers in infinite words</a>, arXiv:1606.02868 [cs.DM], 2016-2018.

%H Gabriele Fici, Antonio Restivo, Manuel Silva, and Luca Q. Zamboni, <a href="https://doi.org/10.1016/j.jcta.2018.02.009">Anti-powers in infinite words</a>, Journal of Combinatorial Theory, Series A 157 (2018), 109-119.

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Dec 18 2019