[seqfan] Re: No loop in view?

[Allan Wechsler]

I suspect that when you remove the initial 1,2,3,0, you get A039982. You
can get many such sequences as the limit of various production rules, and
the output is almost never periodic. Here, the production rules are
something like 0->11, 1->01, with some adjustment at the start of the
sequence.


On Fri, Feb 22, 2019 at 2:58 PM Éric Angelini <bk263401 at skynet.be> wrote:

> Hello SeqFans,
> while I was searching my old messy papers to answer a request
> from Alex Bellos, I've bumped into this idea yesterday:
>
> "The chunks sizes of consonants squeezed between successive
>  pairs of vowels are given by the sequence itself":
>
> ONE, TWO, THREE, ZERO, ONE, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO,
> ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO,
> ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO,
> ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE,
> ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO,
> ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ONE,
> ONE, ZERO, ONE, ONE, ONE, ZERO, ONE, ZERO, ONE, ...
>
> The sequence obviously extends itself forever -- but does it
> enter in a loop at some point?
>
> Jean-Marc Falcoz has computed 30,000 terms and found no loop
> (a third of the terms are 0s, two thirds are 1s). Does someone
> have an idea about the sequence entering at some point in a
> loop -- or never?
> Best,
> É.
> [a copy of this mail was sent to Jean-Marc Falcoz and Neil Sloane]
>
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