[seqfan] Re: Fractal sequence A087088

[Allan Wechsler]

If I were asked to write a sequence title from scratch, I think I would
dispense with "simplest", and say something like "Positive ruler-type
fractal sequence with 1's in every third position." I think only this
sequence satisfies that description.

A "fractal" sequence can be constructed upon any "skeleton" of 1's, as long
as there are an infinite number of entries that are _not_ 1.

On Mon, Jul 13, 2020 at 12:42 PM Neil Sloane <njasloane at gmail.com> wrote:

> Allan, that is an excellent point.  So maybe the sequence should say
> something like "simplest two-step-insertion fractal" ?
>
> 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 Mon, Jul 13, 2020 at 12:37 PM Allan Wechsler <acwacw at gmail.com> wrote:
>
> > To return to the claim of "simplest" sequence with this property; we are
> in
> > the difficult position of trying to read the mind of the person who was
> > making that claim. I think they had some notion of "simplicity" in mind
> for
> > which the statement was arguably true, but as it stands it is hard to see
> > what that notion was. The point about the ruler functions is a strong one
> > -- A001511 can be given a homologous four-step definition exactly
> analogous
> > to the one given for A087088, using gaps of one undefined place instead
> of
> > two. One is simpler than two, isn't it?
> >
> > But even A000027, the positive integers, displays the required property.
> > Remove the only 1; decrement all other entries; behold. In what sense is
> > A087088 simpler than A000027? I think the author(s) had some additional
> > constraints in mind. But if I were shown the title only, and asked to
> > reconstruct the sequence, I would probably produce A000027.
> >
> > On Mon, Jul 13, 2020 at 12:05 PM Frank Adams-watters via SeqFan <
> > seqfan at list.seqfan.eu> wrote:
> >
> > > This sequence and A163491 are ordinal transforms of each other.
> > >
> > > Franklin T. Adams-Watters
> > >
> > >
> > > -----Original Message-----
> > > From: Peter Munn <techsubs at pearceneptune.co.uk>
> > > To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > > Sent: Mon, Jul 13, 2020 9:01 am
> > > Subject: [seqfan] Fractal sequence A087088
> > >
> > > Hello seqfans,
> > >
> > > A087088 claims to be "the simplest nontrivial sequence" such that
> > removing
> > > every "1" gives the same result as adding 1 to every term. Ruler
> > > sequences, such as A001511, share this property, so does anyone have a
> > > clear idea how "simplest nontrivial" might be defined?
> > >
> > > And can anyone shed light on the reason its offset is 3? [1]
> > >
> > > Best Regards,
> > >
> > > Peter
> > >
> > > [1] Apart from the b-file, the rest of the sequence is written as
> though
> > > the offset is 1 (so formulas are strictly incorrect). The relationship
> to
> > > A244040 contributed by Edgar and Van Alstine is neatest with offset 1
> or
> > > offset 0. A relationship I discovered recently (comment in
> > > https://oeis.org/A024629) is clearly neatest if the offset is 1,
> whilst
> > my
> > > work on symmetry (https://oeis.org/history/view?seq=A087088&v=25) and
> > with
> > > A335933 suggests an OEIS-incompatible offset of 1.5 .
> > >
> > > As we are only now starting to refer from other sequences to terms of
> > > A087088, it seems a good time to settle on a good offset. Unless anyone
> > > knows a good reason for keeping it as 3, offset 1 seems better.
> > >
> > >
> > > --
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> >
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