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%I #13 Jul 08 2016 00:11:16
%S 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
%N Largest number of antipower periods possible for a binary string of length n.
%C 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.
%C 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.
%H G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, <a href="http://arxiv.org/abs/1606.02868">Anti-powers in infinite words</a>, arxiv preprint, 1606.02868v1 [cs.DM], June 9 2016.
%e a(18) = 4, as the string 000001010011100101 has antipower periods 3,6,9,18, and no string of length 18 has more.
%Y Cf. A274409, A274449, A274451.
%K nonn
%O 1,2
%A _Jeffrey Shallit_, Jun 23 2016
%E a(19)-a(32) from _Bjarki Ágúst Guðmundsson_, Jul 07 2016
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