[seqfan] Re: No loop in view?

[Allan Wechsler]

I think Eric meant, "What is the lexically first such sequence beginning 1,
2, 3 ... ?" If you leave out the 3, you get 1, 2, 2, 2, ... as Peter says.

Still, Peter's variant takes a lot longer to "calm down", and its
implementation as a production system, though intuitively I know it must
exist, is elusive. My hand calculation says it starts

040205104101104011103101104020310101106 ...

I stopped arbitrarily at the first 6. 6 must be as high as it goes; 6's are
produced by an earlier 03.

I am only just learning Haskell, but I suspect a Haskell program that
produces this sequence can be written in just one or two lines. Something
like

munn :: [Int]
munn = 0 : 4 : drop 2 (countT (drop 2 (spellOut munn)))

... where countT produces the list of the lengths of consonant runs in a
given string, and spellOut converts a list of numbers to a string of
concatenated number names. I'm not quite up to finishing the program.

On Tue, Mar 5, 2019 at 8:44 PM Peter Munn <techsubs at pearceneptune.co.uk>
wrote:

> 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]
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
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