

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
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OFFSET

1,2


COMMENTS

An antiperiod of a lengthn 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{dn} [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

Table of n, a(n) for n=1..32.
G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Antipowers 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

Cf. A274409, A274449, A274451.
Sequence in context: A029238 A345137 A208478 * A126131 A343332 A138012
Adjacent sequences: A274447 A274448 A274449 * A274451 A274452 A274453


KEYWORD

nonn


AUTHOR

Jeffrey Shallit, Jun 23 2016


EXTENSIONS

a(19)a(32) from Bjarki Ágúst Guðmundsson, Jul 07 2016


STATUS

approved



