A303498 Decimal expansion of Sum_{p prime} log(p)/p^8.

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, 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, 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

Offset: 0

Author

Jean-François Alcover, Apr 25 2018

Keywords

• nonn
• cons

Comments

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

Examples

			0.00287952470872924739134602842385733406499898376167586584106761828618532...
		

Links

• Eric Weisstein's MathWorld, Prime Zeta Function
• Wikipedia, Prime Zeta Function

Crossrefs

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).

Programs

Mathematica

RealDigits[PrimeZetaP'[8], 10, 103][[1]]

PARI

suminf(n=1, p=prime(n); log(p)/p^8) \\ Michel Marcus, Apr 25 2018