Guessing the Elusive Patterns in the SlaterValez 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 SlaterValez word
The input gives you
the output.
Pictures

Here is a scatterplot of
the set of points [n,a(n)] where a(n) is the SlaterValez sequence A081145

Here is a scatterplot of
the set of points [n,abs(a(n)a(n1))] where a(n) is the SlaterValez sequence A081145
Personal Journal of Shalosh B. Ekhad and Doron Zeilberger
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