[seqfan] Re: Help with a calculation for A001097 (twin primes)
Charles Greathouse
charles.greathouse at case.edu
Wed Nov 19 17:55:00 CET 2014
The limit diverges to -infinity as -(log^2 n)/3.
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Wed, Nov 19, 2014 at 10:26 AM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:
> Hello Seqfans,
>
> Is there a way to calculate the following limit as n approaches infinity?
> This will be helpful in a comment I intend to add to A001097 (twin primes)
>
> Not sure about the most efficient or best way to notate, so here's what
> I'm asking:
>
> For a(n)>1, let a(n) = A007310 (numbers congruent to 1 or 5 mod 6): 5, 7,
> 11, 13, 17, 19, 23, 25....
>
> So a(1) = 5, a(2) = 7, a(3) = 11 etc.
>
> Calculate 1/a(1) + 1/a(2)*(1 - 1/a(1)) + 1/a(3)*(1 - 1/a(1) - 1/a(2))
> + 1/a(4)*(1 - 1/a(1) - 1/a(2) - 1/a(3))...
>
> So 1/5 + 4/35 + 23/385 + 218/5005 +...
>
> If this is not easily solved, could someone please run a program to get an
> approximation?
>
> Thanks in advance!
>
> Cheers,
> Bob Selcoe
>
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