[seqfan] Re: Fractal sequence A087088

Frank Adams-watters franktaw at netscape.net
Mon Jul 13 18:01:24 CEST 2020

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,


[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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