A303498 - OEIS

%I #7 Apr 26 2018 08:57:09

%S 0,0,2,8,7,9,5,2,4,7,0,8,7,2,9,2,4,7,3,9,1,3,4,6,0,2,8,4,2,3,8,5,7,3,

%T 3,4,0,6,4,9,9,8,9,8,3,7,6,1,6,7,5,8,6,5,8,4,1,0,6,7,6,1,8,2,8,6,1,8,

%U 5,3,2,1,4,8,1,5,4,1,8,3,9,9,5,0,4,8,1,2,7,5,6,6,2,9,6,5,0,6,8,2,7,7,4,7,9

%N Decimal expansion of Sum_{p prime} log(p)/p^8.

%C The negated first derivative of the Prime Zeta function at 8.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_zeta_function">Prime Zeta Function</a>

%e 0.00287952470872924739134602842385733406499898376167586584106761828618532...

%t RealDigits[PrimeZetaP'[8], 10, 103][[1]]

%o (PARI) suminf(n=1, p=prime(n); log(p)/p^8) \\ _Michel Marcus_, Apr 25 2018

%Y Decimal expansion of Sum_{p prime} log(p)/p^k: A136271 (k=2), A303493 (k=3), A303494 (k=4), A303495 (k=5), A303496 (k=6), A303497 (k=7), A303498 (k=8), A303499 (k=9).

%K nonn,cons

%O 0,3

%A _Jean-François Alcover_, Apr 25 2018