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

[Allan Wechsler]

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
>
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