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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..32.

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

Cf. A274409, A274449, A274451.

Sequence in context: A027352 A029238 A208478 * A126131 A138012 A072531

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

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)