[seqfan] Re: When is a sequence a list?

[Neil Sloane]

This discussion started because someone changed the definition of a certain
sequence so that it read:

a(n) sets a new record for the number of 'Reverse and Add' steps needed to
reach a palindrome starting with a(n)


I objected to this for many reasons, but mainly because the sequence was
obviously not an "a(n) = ..." type sequence, but a "Numbers with some
property ..." type sequence. I changed it to:

Indices of record high values in A033665, ignoring those numbers that are
believed never to reach a palindrome.


I think we should end this discussion at this point.

Best regards
Neil

Neil J. A. Sloane, Chairman, 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 Sat, Jul 24, 2021 at 10:45 PM Marc LeBrun <mlb at well.com> wrote:

> I agree this sounds like it's probably being over-thought.  In practice it
> seems pretty simple:
>
> In submitting a sequence, if there's a natural n0 that's the offset, then
> use that, and if not, then make the offset 1.  To elaborate:
>
> If the sequence you are submitting is characterized by some definite
> mapping n-->a(n), and the sequence values you submit start from some n=n0,
> then you should specify the offset as n0.
>
> Otherwise -- eg when index n only means a(n) is "the n-th" instance of
> something, and/or n0 doesn't matter, and/or you can't identify a unique
> natural n0 -- then the default is to make the offset 1.
>
> As a simple example, consider A006933: 2, 4, 6, 30, 32, 34, 36,... the
> "eban numbers", whose English names do not contain the letter E.  There's
> no motivation to associate the initial value 2 with any specific index n0,
> so by convention to avoid confusion we always use the default offset of 1.
>
> Surely that doesn't present much difficulty?
>
> This "default offset=1" situation is colloquially referred to as a "list"
> in the OEIS context -- however the "listness" of a sequence here isn't an
> intrinsic mathematical property of the ordered numerical values, but rather
> a concept that belongs more to the ontology of the OEIS metadata.
>
>
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