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

[Neil Sloane]

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.



is
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



On Fri, Sep 20, 2019 at 4:52 AM Frank Adams-watters via SeqFan <
seqfan at list.seqfan.eu> wrote:

> I did a lot of this some years ago. See https://oeis.org/A118382 and some
> related sequences.
>
> Franklin T. Adams-Watters
>
>
> -----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
>
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