A303493 Decimal expansion of Sum_{p prime} log(p)/p^3.

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

Offset: 0

Author

Jean-François Alcover, Apr 25 2018

Keywords

• nonn
• cons

Comments

The negated first derivative of the Prime Zeta function at 3.

Examples

			0.150757555543950422179836516365342919575501161530689331818797676...
		

Links

• R. Mathar, Series of reciprocal powers of k-almost primes, arXiv:0803.0900 [math.NT], 2008-2009; Table 3, s=3.
• J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV
• 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'[3], 10, 100][[1]]