[seqfan] Re: No loop in view?

[Peter Munn]

Hello Éric,

Of course, there is an earlier sequence satifying the definition: A040000,
which clearly loops: ONE, TWO, TWO, TWO, TWO, TWO, ...

Of greater interest, if 0 is written as NOUGHT, the earliest sequence to
satisfy the definition uses 7 different numbers, each repeatedly,
beginning: NOUGHT, FOUR, NOUGHT, TWO, NOUGHT, FIVE, ONE, NOUGHT, ...

Best Regards,

Peter

On Fri, February 22, 2019 5:19 pm, Éric Angelini 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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