A274449 Number of binary strings of length n having the minimum possible number of different antipower periods.

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

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