[seqfan] May 30 2021 Report

[Neil Sloane]

Dear SeqFans:


1. Gave a talk about OEIS to students who arrived at Rutgers for the summer
program "Research Experience for Undergraduates" (REU). I was going to
mention some recent sequences from the Drafts stack, for example :

A343376 & A343456; A344570; A343369; A344538

and I was going to say:

- it is always worth looking at the"stack", https://oeis.org/drafts,
because there are many interesting sequences there every day, and when you
see something interesting you should think about questions like:

-- is the definition clear? is the sequence well-defined?

-- is the sequence infinite? is there a proof?

-- how fast does it grow?

-- does every number appear?

-- is there a formula or generating function?

-- how would you write a program to generate it?

- If the sequence entry doesn't answer these questions, and you can, you
should submit a comment to the entry (of course you should register).
Getting your name into the OEIS is something to be proud of.

It was a Zoom talk, so of course there were technical problems, and nothing
went as planned. Most of it was recorded.  The sequences I mentioned are
probably still worth investigating.


1a: To find other worthwhile problems to work on, in the OEIS search
window, enter "It would be nice", or "Conjecture", or "Empirical".


1b. Or, start at a recent sequence, say A344555 (interesting sequence, by
the way), and walk backwards through the recently accepted sequences. By
that I mean, enter A344555 in the search window, then when it appears,
click on its A-number. This will show the "Adjacent sequences" link at the
bottom. Now you can walk backwards through the OEIS.


2. Ali Sada's recent question on this list led me to the almost-core
sequence A011772, the smallest m such that m(m+1)/2 is divisible by n. It
is interesting because it is a basic question and it does not have a simple
answer. There is no simple formula for a(n). Look at the graph. I don't
even have an adjective to describe it. Yet I've seen many other sequences
with a similar graph. The Index to the OEIS has an entry for:

Graphs (or plots) , sequences with interesting:

that gives names ("Tornado", etc)

but A011772 is not listed (as I said, there's no name for this graph).


3.  So I was thinking - and I was almost going to mention this to the
students - us OEIS folks spend a lot of time staring at some sequence,
trying to figure out what is going on.  Looking for any kind of formula,
and ANYTHING that would help understand it (see example in next paragraph).
It might be helpful if we had some way of grouping sequences according to
their graphs. The EKG sequence for example is basically three straight
lines of different slopes. The Yellowstone permutation is similar but has
more lines. Superseeker might have a component that would tell you "Your
sequence has a graph which is rather like the graphs of the following
sequences ..."  If there as a close match that might be really helpful.


4. Quite often when working on a problem I come across a sequence with a
simple definition that is easy to generate but has no formula, and
Superseeker doesn't help.

There are several examples in this paper that we recently finished revising:

Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration
and Stained Glass Windows, 1: Rectangular Grids, Preprint, revised May 21
2021, http://neilsloane.com/doc/rose_5.pdf,


for example A334701, the number of simple interior nodes in the graph
BC(1,n). We have 500 terms, but no formula!

See Table 6 in the paper, or A334701.

Following the example of one of my friends: if you can find a formula for
A334701, I will donate $100 to the OEIS Foundation in your name. (See
http://oeisf.org/#DONORS.)


5. Do we have any Mac experts here? I do all my work in xterm windows, and
vim suddenly stopped working. I was unable to install a new version using
Homebrew. I am running High Sierra 10.13.6. If you could help, send me an
email.


Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com