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A317167 Number of distinct critical exponents possible, over all binary strings of length n. 1
1, 2, 3, 3, 5, 6, 9, 11, 14, 16, 20, 21, 27, 30, 33, 36, 44, 47, 55, 58 (list; graph; refs; listen; history; text; internal format)
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.  The critical exponent of a string x is the maximum, over all nonempty contiguous subwords w of x, of exp(w).

LINKS

Table of n, a(n) for n=1..20.

EXAMPLE

For n = 6, there are 5 possible critical exponents:  6 (for 000000), 5 (for 000001), 4 (for 000011), 3 (for 000111), 2 (for 001001), and 5/2 (for 001010).

CROSSREFS

Sequence in context: A300446 A039876 A239312 * A070830 A039862 A018051

Adjacent sequences:  A317164 A317165 A317166 * A317168 A317169 A317170

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Jul 23 2018

STATUS

approved

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Last modified September 24 12:20 EDT 2020. Contains 337318 sequences. (Running on oeis4.)