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A274450
Largest number of antipower periods possible for a binary string of length n.
4
1, 2, 1, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 3, 3, 1, 4, 1, 4, 3, 2, 1, 6, 2, 2, 2, 4, 1, 5, 1, 4
OFFSET
1,2
COMMENTS
An antiperiod of a length-n string x is a divisor l of n such that if you factor x as the concatenation of (n/l) blocks of length l, then all these blocks are distinct.
It seems very likely that this sequence is sum{d|n} [n/d <= 2^d] where [...] is the Iverson bracket that is 1 if the condition is true and 0 otherwise, but I don't have a proof yet.
LINKS
G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Anti-powers in infinite words, arxiv preprint, 1606.02868v1 [cs.DM], June 9 2016.
EXAMPLE
a(18) = 4, as the string 000001010011100101 has antipower periods 3,6,9,18, and no string of length 18 has more.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 23 2016
EXTENSIONS
a(19)-a(32) from Bjarki Ágúst Guðmundsson, Jul 07 2016
STATUS
approved