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Problem with a limit.

• To: mathgroup at smc.vnet.net
• Subject: [mg66759] Problem with a limit.
• From: Roger Bagula <rlbagulatftn at yahoo.com>
• Date: Mon, 29 May 2006 06:05:51 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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.

• Follow-Ups:
  • Re: Problem with a limit.
    • From: danl@wolfram.com