A274457 Shortest possible antipower period of a binary string of length n.

1, 1, 3, 2, 5, 2, 7, 2, 3, 5, 11, 3, 13, 7, 3, 4, 17, 3, 19, 4, 3, 11, 23, 3, 5, 13, 9, 4, 29, 5, 31, 4, 11, 17, 5, 4, 37, 19, 13, 4, 41, 6, 43, 4, 5, 23, 47, 4, 7, 5, 17, 4, 53, 6, 5, 4, 19, 29, 59, 4, 61, 31, 7, 4, 5, 6, 67, 17, 23, 5, 71, 6, 73, 37, 5, 19, 7, 6, 79, 5, 9, 41, 83, 6, 5, 43, 29, 8, 89, 5, 7, 23, 31, 47, 5, 6, 97, 7, 9, 5, 101, 6, 103, 8, 5, 53

Offset

1,3

Comments

An antiperiod of a length-n string x is a divisor d of n such that if you factor x as the concatenation of (n/d) blocks of length d, then all these blocks are distinct.

k*2^k (A036289(k)) is the largest number n that makes a(n) = k. - Jinyuan Wang, Feb 15 2019

Links

Jinyuan Wang, Table of n, a(n) for n = 1..10000

G. Fici, A. Restivo, M. Silva, and L. Q. Zamboni, Anti-powers in infinite words, arxiv preprint, 1606.02868v1 [cs.DM], June 9 2016.

Formula

a(n) is the smallest divisor d of n such that n/d <= 2^d.

Mathematica

a[n_] := Do[If[n/d <= 2^d, Return[d]], {d, Divisors[n]}];
Array[a, 106] (* Jean-François Alcover, Feb 15 2019 *)

Prog

(PARI) a(n) = fordiv(n, d, if (n/d <= 2^d, return (d))); \\ Michel Marcus, Feb 15 2019

Crossrefs

Cf. A036289, A274409, A274449, A274450, A274451.

Sequence in context: A023513 A069735 A358536 * A328579 A046524 A086571

Adjacent sequences: A274454 A274455 A274456 * A274458 A274459 A274460

Keyword

nonn

Author

Jeffrey Shallit, Jun 23 2016

Status

approved