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MathGroup Archive 2006

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Re: Problem with a limit.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66779] Re: Problem with a limit.
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Tue, 30 May 2006 05:48:21 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e5ei0n$7to$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Roger Bagula wrote:
> This sum works really well:
> 
> a = Sum[(PrimePi[k + 1] - PrimePi[k])/2^k, {k, 1, Infinity}]
> 
> I got the idea to look at it from the other end as
> primes dominate the low end of the Integers:
> 
>   Limit[Sum[(PrimePi[k + 1] - PrimePi[k])/2^(n - k), {k, 1, n}], n -> 
> Infinity]
> 
> So I tried:
> 
> Table[N[Limit[Sum[(PrimePi[ k + 1] - PrimePi[k])/2^(n - k), {k, 1, n}], 
> n ->10^m], {m, 1, 10}]
> 
> 
> It's just an interesting problem in how the primes are distributed.
> 
Hi Roger,

I am not sure what the question is, since the sum returned unevaluated 
and the last command -- Table[xxx] -- returns a couple of error 
messages. Perhaps you can try

In[2]:=
Table[N[Sum[(PrimePi[k + 1] - PrimePi[k])/
      2^(10^n - k), {k, 1, 10^n}]], {n, 1, 5}]

Out[2]=
                                        -9
{1.08398, 1.06275, 0.0634804, 3.7835 10  , 0.0012207}

I hope I have not missed the point.

Best regards,
Jean-Marc


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