[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?.

Me: Among first 2000 a(n)'s there are 26 primes, with first ones:

{n,a(n)=prime}
{1,2}
{2,3}
{3,11}
{4,17}
{8,283}
{9,547}
{10,1069}
{27,5546789}

and the last (sorry for flood, just for curiosity...)
{1587,34433593933173758897542097304460383970179380216590984978253779982639407351684922883979342682677346080515956517823}

zak