[seqfan] Re: Help with a calculation for A001097 (twin primes)

[Charles Greathouse]

Oops, that's 9, not 3.

The sum reaches a maximum at 0.5457808... at a(n) = 65 and passes 0 at a(n)
= 1513.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Nov 19, 2014 at 11:55 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> 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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>>
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>>
>
>