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MathGroup Archive 2010

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Hurwitz Zeta Rational Sequence showing primes in the denominator

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110079] Hurwitz Zeta Rational Sequence showing primes in the denominator
  • From: GHMM <ghfmlm at googlemail.com>
  • Date: Tue, 1 Jun 2010 04:22:55 -0400 (EDT)

I've been looking at a zeta function to produce the primes and have
come up with the following:

Table[D[FindSequenceFunction[Table[Rationalize[ i^m N[Zeta[1 - m, (-i
- 1)/i] + Zeta[1 - m, -(1/i)], 80]], {i, 80}] , n],{n, m}], {m, 30}]

output :

2, 5/3, 6, 122/5, 120, 5000/7, 5040, 40656, 362880, 39312000/11,
39916800, 6489711360/13, 6227020800, 72648576000, 1307674368000,
671011307366400/17, 355687428096000, -(621352061890560000/19),
121645100408832000, 131163645205064908800, 51090942171709440000, -
(14526772739252431257600000/23)...

Can someone please help to fit the numerators of this rational
sequence into a product, the denominators are the primes.

Ray


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