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A307541
a(n) is the smallest number k such that every binary string of length >= k contains either a cube or an n-anti-power.
0
1, 3, 9, 19, 41, 58, 86
OFFSET
1,2
COMMENTS
A k-power is k consecutive identical blocks. A 3-power is called a cube. A k-anti-power is k consecutive distinct blocks of the same length.
LINKS
G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Anti-Powers in Infinite Words, arXiv:1606.02868 [cs.DM], 2016-2018.
EXAMPLE
For n = 3, the binary string 00101001 of length 8 contains neither a cube nor a 3-anti-power. But every binary string of length >= 9 does contain either a cube or a 3-anti-power, so a(3) = 9.
CROSSREFS
Sequence in context: A146441 A147341 A208972 * A268403 A241626 A160704
KEYWORD
nonn,base,more
AUTHOR
Samin Riasat, Apr 13 2019
STATUS
approved