sum of 1/A007504(n)
Don Reble
djr at nk.ca
Wed May 16 19:28:18 CEST 2007
Stefan Steinerberger wrote:
> Let f_n be the sum of the first n primes. Then it is easy to see that
> f_n = 2 + 3 + 5 ... + p(n) > 1 + 3 + 5 + ... + (2n-1) = n^2
>
> Now we use this argument to get an upper bound for
> Sum[1/f_n, {i, 10^4 + 1, oo}]
Using a slight improvement of that idea, and my CDrom full of
primes, I can determine that
1.023476323822197 < X < 1.023476324054903
Argggh! It's only a microtwitch away from the next digit.
Does anyone know how to calculate the digamma function, _very_
accurately, for arbitrary (irrational) arguments?
--
Don Reble djr at nk.ca
--
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