[seqfan] Re: polynomial-to-product transform

[zak seidov]

--- 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