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A274449 Number of binary strings of length n having the minimum possible number of different antipower periods. 4
2, 2, 8, 4, 32, 2, 128, 16, 176, 32, 2048, 4, 8192, 128, 2348, 256, 131072, 8, 524288, 424, 47824, 2048, 8388608, 16, 9389312, 8192, 785408, 11680, 536870912, 2, 2147483648, 65536 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An antipower period 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. For example, 011010010 has antipower period 9 only, which is the least possible for a string of length 6, while 011010001 has two antipower periods 3 and 9, which is the most possible for a string of length 9.

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.

CROSSREFS

Cf. A274409, A274450, A274451.

Sequence in context: A103839 A135727 A320423 * A333711 A075101 A075103

Adjacent sequences:  A274446 A274447 A274448 * A274450 A274451 A274452

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 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)