[seqfan] Re: A191476 2^i*3*j and A134583 dimensions of cantor set

[Neil Sloane]

So those two (A191476 and A134583) should be merged - and several related
sequences (A022329, A  3586, etc) need to be edited.   This looks like
something I need to do myself.

I will start on it later today.

But if any of you (Richard, Amiram, Allan, ... ) want to send me
suggestions about changes that need to be made, and the best way to handle
this, please do so!

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com



On Sun, May 26, 2024 at 2:44 PM Allan Wechsler <acwacw at gmail.com> wrote:

> In the description of A134583, the reference to the Haussdorff dimension of
> the Cantor set is, in my opinion, superfluous, and only makes people who
> don't happen to have studied fractals feel like they don't understand this
> sequence. The sequence is really about the irrational number log 2 / log 3;
> let's call that number H.
>
> Consider all the numbers of the form a + bH, where a and b are positive
> integers. The smallest one is 1 + H (a = b = 1). The next smallest is 1 +
> 2H (a = 1, b = 2). The next is 2 + H (a = 2, b = 1). All the numbers of
> this form can be sorted into increasing order (there are no cluster points
> or other obstacles to this). If you read off the a-values, this forms
> the *signature
> sequence *of H.
>
> I agree with Amiram Eldar's conclusion that these two sequences can easily
> be proved identical (Amiram posted while I was typing this.)
>
> On Sun, May 26, 2024 at 1:03 PM Richard J. Mathar <mathar at mpia-hd.mpg.de>
> wrote:
>
> > The comments in A191476 (concerning the ordered sequence of 2^i*3^j) and
> > A134583 (Haussdorff dimension of which I don't know anything...) say that
> > the sequences differ. The first 1000 terms of the b-files are the same.
> > At which index/position start these sequences to differ?
> >
> > --
> > Richard Mathar
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
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