Guessing the Elusive Patterns in the Slater-Valez sequence (aka OEIS A081145)

By Shalosh B. Ekhad and Doron Zeilberger

.pdf   .ps   .tex

(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)

Written: 28 Iyyar, 5779.

Dedicated with admiration and friendship to Aviezri S. Fraenkel (b. 28 Iyyar, 5689 [June 7, 1929, according to their reckoning])

מ ו ק ד ש   ל מ ו ר י   ו ר ב י  ,   א ב י ע ז ר י   פ ר נ ק ל  ,   ב מ ל א ת   ל ו   צ'   ש נ י ם

This short note, dedicated with admiration and friendship to one of our gurus, Aviezri Fraenkel, uses what he taught us many years ago in order to study the intriguing OEIS sequence A081145, brought to our attention by another one of our gurus, Neil Sloane .

## Maple package

SlaterValez.txt.
[You would also need the data set DataSlaterValez.txt.]

## Sample Input and Output Files

• If you want to see an esimate for the transition probability from state 2 to state 1(under the heuristic assumption) (in the convention of the article) and the implied slopes
The input gives you the output.

• If you want to see the first 150000 terms of the Slater-Valez word
The input gives you the output.

## Pictures

• Here is a scatter-plot of the set of points [n,a(n)] where a(n) is the Slater-Valez sequence A081145

• Here is a scatter-plot of the set of points [n,abs(a(n)-a(n-1))] where a(n) is the Slater-Valez sequence A081145

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger