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

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

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