Proof needed

[Joerg Arndt]

Lesson learned???

Again the  Recognize[ something-numerical ]  nonsense!

And see:  http://www.research.att.com/~njas/sequences/A047219

Another point very much against this sort of bad random number
generators is that you are using base-10.


* Artur <grafix at csl.pl> [Mar 18. 2008 09:57]:
> Dear Seqfans
> Who have idea how to prove:
> Some numbers are giving empty set in this procedure. These numebrs are e.g.
> Golden Ratio=(1+Sqrt[5])/2, Sqrt[2] what mean that if you need improove 
> accuracy one decimal digit we have to uses new fraction with bigger 
> integers as numerator and denominator.
>
> Method bellow
>
> Any comment appreciated
> BEST WISHES
> ARTUR
>

Moreover...

>
> %N A138373 Positions of digits after decimal point of number Sqrt[5]/2 
> where the approximation to this number by rational fraction does not 
> improve the accuracy.

What "rational fraction" approximation do you mean?
The digits/10^N one?



> %C A138373 Some numbers are giving empty set in this procedure.

Which procedure?
If you think that one line of computer algebra code with partly
undefined behavior is useful for more than casual experimentation
then you are badly mistaken.

Note "encyclopaedia" =!= "collection of random observations"



> These 
> numebrs are e.g.
> Golden Ratio=(1+Sqrt[5])/2, Sqrt[2] what mean that if you need improove 
> accuracy one decimal digit we have to uses new fraction with bigger 
> integers as numerator and denominator.

Definitely have your description's spelling and semantics checked
before submitting!  You inflict a work load on the editors that
can be avoided with minimal effort on your side.



> For all numbers sequence is that 
> same also for 1/number.
> %e A138373 a(1)=3 because 38/7 approximate Pentanacii constant to 2 and 
> also to 3 digits
> %t A138373 << NumberTheory`Recognize`
> b = {}; a = {}; Do[k = Recognize[N[Sqrt[5]/2, n + 1], 1, x]; If[MemberQ[a, 
> k], AppendTo[b, n], AppendTo[a, k]], {n, 1, 500}]; b (*Artur Jasinski*)

I sincerely hope that these ...

> %Y A138373 A138335, A138336, A138337, A138338, A138339, A138343, A138366, 
> A138367, A138368, A138369, A138370, A138371, A138372, A138374, A138375, 
> A138376, A138377, A138378, A138378, A138379

... are not more of this type of sequence to come.


> %O A138373 1
> %K A138373 ,base,nonn,
> %A A138373 Artur Jasinski (grafix at csl.pl), Mar 17 2008


...so make a comment in A047219 (but with proper definition of your
operation) and refrain from admitting your usage of Recognize[]
in the public.


best regards,   jj