[seqfan] Re: polynomial-to-product transform

Robert Israel israel at math.ubc.ca
Sun Nov 9 23:41:32 CET 2008

```I get a pretty fair fit to
a(i) = exp(2.19036803533774814*i^.647754651815683258)
which would indicate the limit should be 0.

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

On Sun, 9 Nov 2008, zak seidov wrote:

> --- On Sun, 11/9/08, Neil Fernandez <primeness at borve.org> wrote:
>
>
>> 1) a product-to-polynomial transform on the primes gives:
>>
>> (1+2x)(1+3x^2)(1+5x^3)(1+7x^4)(1+11x^5)...=
>> 1+2x+3x^2+11x^3+...
>>
>> and the sequence beginning
>>
>> {2,3,11,17,40,86,153,283,547,1069,1737,3238,5340,9574,17251,27897,45845,
>> 78601,126725,207153,...}
>>
>> Does a(n)/a(n-1) tend to a constant?
>
> Up to n=2000,
> a(n)/a(n-1) is (more o less) monotonically decreasing
> with last 10 values:
>
>  a(n)/a(n-1) for n=1991-2000
>  1.099162919652222,
>  1.099142077551366,
>  1.0991212743371226,
>  1.0991004615883713,
>  1.0990796900413804,
>  1.0990589060030618,
>  1.0990381642409315,
>  1.099017411687622,
>  1.0989966981648613,
>  1.0989759756749997,
>
> zak
>
>
>
>
>
>
>
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```