[seqfan] Re: Fractal sequence A087088

[Neil Sloane]

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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