[seqfan] Re: Fractal sequence A087088

[Peter Munn]

Thank you, Frank, for the reference, and Allan, for clarifying the issues.
I guess A000027 may have been a sequence the A087088 author considered
trivial. The intent of "simplest" remains unclear, and I am content it has
been removed from the name. I suppose we might say A087088 is the simplest
nontrivial sequence with the stated property and with positions of ones
having density less than 1/2.

Peter

On Mon, July 13, 2020 7:28 pm, Allan Wechsler wrote:
> 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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