[seqfan] Re: Look left and say

[Benoît Jubin]

It may be more natural to include descriptions like "there are 0 two's so
far", and start with the empty sequence. This gives:
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20,
23...
The sequence is injective as well, with probably the same asymptotics,
which seems to grow like Theta(n.log(n)) with a fractal behavior (I plotted
the first 2,000,000 terms to get an idea).

Benoît

On Fri, Nov 15, 2019 at 1:05 AM <israel at math.ubc.ca> wrote:

> Should that not be S = 0, 10, 11, 20, 12, 22, 30, 13, 23, 33, 40, 14, 24,
> 34, 44, 50, 15, 25, 35, 45, 55, 60, 16, 26, 36, 46, 56, 66, 70, 17, 27,
> 37,
> 47, 57, 67, 77, 80, 18, 28, 38, 48, 58, 68, 78, 88, 90, 19, 29, 39, 49,
> 59,
> 69, 79, 89, ...?
>
> Thus after after 23 you can have 33 (three 3's) rather than 40 (four 0's).
>
> Cheers,
> Robert
>
>
> On Nov 14 2019, Éric Angelini wrote:
>
> > Hello SeqFans, S = 0, 10, 11, 20, 12, 22, 30, 13, 23, 40, 14, 24, 34,
> 44,
> > 50, 15, 25, 35, 45, 55, 60, 16, 26, 36, 46, 56, 66, 70, 17, 27, 37, 47,
> > 57, 67, 77, 80, 18, 28, 38, 48, 58, 68, 78, 88, 90, 19, 29, 39, 49, 59,
> > 69, 79, 89, 93,...
> >
> >Pick any term (except the first one) - for instance 93
> >(at the end); this 93 says "On my left, there are
> >9 digits "3", altogether. Which is correct: from 0 to 89
> >(both markers included) there are exactly nine digits 3 in S.
> >
> >S is always extended with the smallest integer that
> >"says the truth" about the past of S.
> >S is started with a(1) = 0.
> >
> >Could someone compute more terms and submit S to the OEIS
> >if S is not already there - with another a(1), for instance -
> >and if S is of interest?
> >
> >The second part of this mail is here (with another seq proposal):
> >https://bit.ly/2CKDqFk
> >Best,
> >É.
> >
> >--
> >Seqfan Mailing list - http://list.seqfan.eu/
> >
> >
>
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