[seqfan] Re: Representation of real numbers by sequences

Oscar Cunningham mail at oscarcunningham.com
Mon May 18 16:08:51 CEST 2020

On 18/05/2020 13:07, Olivier Gerard wrote:
> On Mon, May 18, 2020 at 3:01 PM Oscar Cunningham <mail at oscarcunningham.com>
> wrote:
>> There has also been some interesting discussion of this blog post on
>> reddit
>> (
>> https://old.reddit.com/r/math/comments/glhu6f/a_better_representation_for_real_numbers/),
>> in which someone pointed out that the sequence 0,1,2,3,... corresponds
>> under this representation to the real number J_0(2)/J_1(2) where J is
>> the Bessel function.
> Sorry but I fail to see the point.
> The CF of J_0(2)/J_1(2)  as well as the CF of several constants of this
> kind is already very simple
> As CFs of ratios of Bessel goes,  J_0(2)/J_3(2) is even better.
> The integers interleaved with a constant 1, without a prefix.

The point wasn't to represent any particular real number. Instead my 
objective was to make a system that could represent every real number in 
a uniform way, without having to worry about special cases or 
nonuniqueness of the representations. The fact that certain closed form 
expressions correspond to nice sequences is just an added bonus.

On 18/05/2020 13:48, Giovanni Resta wrote:
> Yes, I've seen the reddit post and the blog, it seems really interesting.
> Probably you should add a link to your relevant web page in 
> https://oeis.org/A301484 .

Thanks! I will do. Is it okay for me to link to my own blog from a 
comment on the OEIS? It seems a bit bigheaded. :-)


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