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A274450
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Largest number of antipower periods possible for a binary string of length n.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(18) = 4, as the string 000001010011100101 has antipower periods 3,6,9,18, and no string of length 18 has more.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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