A274450 Largest number of antipower periods possible for a binary string of length n.

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

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: A029238 A345137 A208478 * A366979 A126131 A343332

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