A274409 Number of binary strings of length n having the maximum possible number of different antipower periods.

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

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