Zeta(1+s)
I can't find anything about it on the web, so I'll post a question here:
What is known about the series expansion of Zeta(1+s) when s gets near zero? I found Zeta(1+s) = 1/s + Gamma + s/13.73327...  s²/206.39...  s³/2921.6... + ... (Maybe I have some more questions or results of other calculations of mine I'll post on this thread later on.) 
[url]http://mathworld.wolfram.com/StieltjesConstants.html[/url]

Darn, I really should read more carefully; I've been on this site before. Sorry.
Now to something completely different  was someone ever interested in the sum of reciprocals of full reptend primes ([URL]http://mathworld.wolfram.com/FullReptendPrime.html[/URL])? I figured the sum 1/7+1/17+1/19+... exceeds 1 at about p=10.7*10^9. General formula: Sum[SIZE=1](f.r.p.)[/SIZE][SIZE=2](1/p) ~ (log log p  0.4655)*Artin's constant.[/SIZE] Any objections? Formulae for bases other than 10? 
Yes, the sum should be
Artin*(log log p) + O[1] 
[quote=XYYXF;161535]Yes, the sum should be
Artin*(log log p) + O[1][/quote] I suppose that's equivalent to Artin*(log log p + c) (± prime number irregularities) for some constant c for each base b. At least until I'm more familiar with the niceties of the bigoh notation. 
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