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A264689 Minimum of the Kamae-Xue measure of randomness for binary strings of length n. 0
1, 3, 8, 14, 23, 35, 50, 66, 85, 107, 134, 162, 193, 227, 264, 302, 343, 387, 436, 488 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The Kamae-Xue measure of a word is the sum of the squares of the number of occurrences of each distinct factor (contiguous subword) of w.

LINKS

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

Teturo Kamae and Yu-Mei Xue, An Easy Criterion for Randomness, Sankhya: The Indian Journal of Statistics, 2015, Volume 77-A, Part 1, pp. 126-152, DOI:10.1007/s13171-014-0054-3.

Teturo Kamae and Dong Han Kim, A characterization of eventual periodicity, Theoretical Computer Science 581 (2015) 1-8, doi:10.1016/j.tcs.2015.02.039.

EXAMPLE

Examples of strings achieving this minimum are 0, 01, 010, 0110, 00110, 001101, 0011010, 01001110, 011100010, 0101110001, 01011100010, 010111000110.

CROSSREFS

Sequence in context: A098762 A014848 A140479 * A146158 A062354 A257644

Adjacent sequences:  A264686 A264687 A264688 * A264690 A264691 A264692

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Nov 21 2015

STATUS

approved

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Last modified August 4 09:03 EDT 2020. Contains 336201 sequences. (Running on oeis4.)