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A274409 Number of binary strings of length n having the maximum possible number of different antipower periods. 4
2, 2, 8, 12, 32, 18, 128, 24, 336, 992, 2048, 1348, 8192, 16256, 6060, 43680, 131072, 20160, 524288, 429528, 39248, 4192256, 8388608, 15632, 24165120, 67100672, 133432320, 54894172, 536870912, 555642580, 2147483648, 518918400 (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, 000110 has antipower periods 2,3, and 6, which is the most possible for a string of length 6, while 000001 has antipower periods 3 and 6 only.

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. A274449, A274450, A274451.

Sequence in context: A254219 A053414 A189837 * A302118 A014236 A087955

Adjacent sequences:  A274406 A274407 A274408 * A274410 A274411 A274412

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 November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)