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A274457
Shortest possible antipower period of a binary string of length n.
1
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
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
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jun 23 2016
STATUS
approved