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Decimal expansion of Sum_{p prime} log(p)/p^9.
8

%I #7 Apr 26 2018 08:58:52

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

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

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

%N Decimal expansion of Sum_{p prime} log(p)/p^9.

%C The negated first derivative of the Prime Zeta function at 9.

%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 0.0014104919214245312915541964563081999779016571316934961928365008287798...

%t RealDigits[PrimeZetaP'[9], 10, 103][[1]]

%o (PARI) suminf(n=1, p=prime(n); log(p)/p^9) \\ _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 0,4

%A _Jean-François Alcover_, Apr 25 2018