[seqfan] Re: Brute force density: triples and cubes
M. F. Hasler
oeis at hasler.fr
Thu Oct 2 20:43:31 CEST 2014
Concerning possible variants, I propose
https://oeis.org/draft/A248153 with initial term a(0)=10
and multiplication by 7 instead of 3.
(Eric's original sequence is now at oeis.org/A248128 ;
those who have given it a thought have understood that the seemingly
arbitrary a(0)=50 is the smallest choice to have digits 0 and 5
occurring in the sequence, which they don't if not in a(0);
multiplying by 7 does not require 5 to be in a(0) in order to occur later.)
On Thu, Oct 2, 2014 at 12:53 AM, M. F. Hasler <oeis at hasler.fr> wrote:
> Eric, (...)
> I think it's easy to show that the distance between zeros is strictly
> increasing, which excludes existence of a loop,
> and also implies that the asymptotic density of "0" (as well of "5"
> which only occurs immediately before a "0") is zero.
> The other digits seem to occur with relative densities of about
> 19%, 21%, 13%, 7%, 14%, 6%, 10% and 9%.
> This can be computed to arbitrary precision by constructing the
> limiting sequence Bob pointed out,
> On Wed, Oct 1, 2014 at 9:12 AM, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>> Hello SeqFans,
>> is T containing 10% of 0s, 10% of 1s, 10% of 2s,... 10% of 9s?
>> T starts with 50 and is always extended with the triple of the
>> leftmost digit not yet tripled in T.
>> T = 50,15,0,3,15,0,9,3,15,0,27,9,3,15,0,6,21,27,9,3,15,0,18,6,3,6,21,27,9,3,15,0,3,24,...
>> (if T enters into a loop, the question is closed -- but I can't
>> find one).
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