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A264689 Minimum of the Kamae-Xue measure of randomness for binary strings of length n. 0

%I #17 Nov 21 2015 14:52:20

%S 1,3,8,14,23,35,50,66,85,107,134,162,193,227,264,302,343,387,436,488

%N Minimum of the Kamae-Xue measure of randomness for binary strings of length n.

%C 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.

%H Teturo Kamae and Yu-Mei Xue, <a href="http://www14.plala.or.jp/kamae/RandomnessCriterion.pdf">An Easy Criterion for Randomness</a>, Sankhya: The Indian Journal of Statistics, 2015, Volume 77-A, Part 1, pp. 126-152, DOI:10.1007/s13171-014-0054-3.

%H Teturo Kamae and Dong Han Kim, <a href="http://www14.plala.or.jp/kamae/Periodicity.pdf">A characterization of eventual periodicity</a>, Theoretical Computer Science 581 (2015) 1-8, doi:10.1016/j.tcs.2015.02.039.

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

%K nonn,more

%O 1,2

%A _Jeffrey Shallit_, Nov 21 2015

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)