[seqfan] Re: Possible other integer sequences for Šindel sequences?

[M. F. Hasler]

On Sat, Sep 21, 2019 at 1:40 PM Neil Sloane wrote:

> Frank A.-W. asks:
> > Does adding a sequence to the OEIS with appropriate discussion constitute
> > publication?
>
> In my opinion, yes. We've been around a long time, and there are 8000 or
> more references to us in the literature. Something like:
>
> A. B. Smith, Sequence A123456, On-Line Encyclopedia of Integer Sequences
> (often with the URL and/or the submission date).
> is a perfectly OK reference in any journal.
>

I agree - OEIS sequences *are* published, anyway,
but more than that, most of them are peer-reviewed
since the advent of the OEIS wiki with associate editors.

Prior to that, they had been published as part of Neil's books
(those have the status of publications in a book)
or, in between, by Neil himself in the OEiS v.1.0 :
those are the only ones that have been published only on internet and not
"peer reviewed" in a stricter sense.
(In only a few special cases sequences are still today published without
peer review. The editing history shows whether (and sometimes why) this is
the case, for each concrete example.)

- Maximilian


> -----Original Message-----
> From: C.R. Drost <c.r.drost at gmail.com>
> To: seqfan <seqfan at list.seqfan.eu>
> Sent: Thu, Sep 19, 2019 10:08 pm
> Subject: [seqfan]       Possible other integer sequences for
Šindel sequences?
>
> Hi there!
> I recently became interested in the Orloj sequence
https://oeis.org/A028355
> which is really a sequence of decimal interpolations of sequences. There
is
> a nice paper linked about all of the other sequences than 1-2-3-4-3-2 that
> have this remarkable property, like 1-2-2, where successive takes of the
> repetition of the sequence can sum to the counting numbers,
>
> 1, 2, 2+1, 2+2, 1+2+2, 1+2+2+1, 2+2+1+2, 2+1+2+2+1, ...
>
> the key to the proof being that every later number like 11 can be viewed
as
> (the construction for 1) + (2 periods of the sequence). The paper calls
> these Šindel sequences and has a nice set of constructions for them that
do
> not require enumerating something like n! sequences of length n and
> checking for a proof that they cover all the integers, but just starts
from
> the sum: it turns out that the sum of the digits uniquely specifies the
> sequence up to a process of "breakup" where e.g. 1-2-2 becomes 1-2-1-1 or
> 1-1-1-2 and eventually 1-1-1-1-1; you can always break apart one term in
> any Šindel-sequence into two more that sum to the same.
>
> It looks like these are pleasantly unrelated to anything else in OEIS and
> I'd like to add some integer sequences, I am just struggling with how to
> define what I am adding :)
>
> I could do the number of primitive Šindels of length n, this seems to stay
> low and erratic,
>
> 0, 1, 2, 1, 4, 0, 3, 1, 5, 1, 1, 2, 7, 0, 2, 1, 7, 0, 3, 1, 2, 2, 5, 0,
12,
> 0, 0, 2, 4, 0, 4, 2, 8, 1, 1, 0, 8, 1, 2, 0, 5, 0, ...
>
> One thing I don't like about this sequence is that the logical outpouring
> of the math for primitive Šindels causes the primitives to include a bunch
> of things that I think are kind of "cheating", for example those two
> 2-periodic sequences are 1-1-1-1-1-1-1-... and 1-2-1-2-1-2-... and I feel
> like the first has already been counted in some sense; it is not
*strictly*
> 2-periodic. (That is, I consider the sequences to be infinite sequences,
> not finite chunks to be repeated.) So if I am chasing strict periodicity
> then I need to abandon the notion of primitive Šindels and instead get a
> count of strictly-n-periodic Šindels,
>
> 0, 1, 1, 1, 4, 10, 14, 29, 62, 146, 293, 610, 1139, 2070, ...
>
> would either of these be interesting submissions to OEIS? Should I abandon
> the notion of strict periodicity so that each term contains the sum of the
> term for that number in the above sequence plus the terms for all of its
> factors? Etc.
>
> -- Chris