

A317177


Number of distinct circular critical exponents possible, over all binary strings of length n.


0



1, 2, 2, 3, 4, 5, 7, 9, 10, 13, 16, 18, 22, 25, 27, 31, 38, 37
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OFFSET

1,2


COMMENTS

A string x has period p if x[i]=x[i+p] for all i that make sense. The shortest period is called "the" period. The exponent exp(x) of a string x of length n is defined to be n/p, where p is the period. Two words are conjugates if one is a cyclic shift of the other. The circular critical exponent is the maximum, over all contiguous subwords w of all conjugates of x, of exp(w).


LINKS

Table of n, a(n) for n=1..18.


EXAMPLE

For n = 7, the a(7) = 7 circular critical exponents possible are 7 (from 0000000); 6 (from 0000001); 5 (from 0000011); 4 (from 0000101); 3 (from 0001001); 7/3 (from 1001001); and 7/2 (from 0101010).


CROSSREFS

Cf. A317167.
Sequence in context: A134727 A152305 A131419 * A326491 A266748 A304883
Adjacent sequences: A317174 A317175 A317176 * A317178 A317179 A317180


KEYWORD

nonn,more


AUTHOR

Jeffrey Shallit, Jul 23 2018


STATUS

approved



