[seqfan] Re: Fractal sequence A087088

Allan Wechsler acwacw at gmail.com
Mon Jul 13 18:20:40 CEST 2020

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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