A373809 Decimal expansion of the second derivative P''(2) of the prime zeta function at 2.

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

Offset: 0

Author

R. J. Mathar, Aug 18 2024

Keywords

• nonn
• cons

Examples

			0.74159785498280500302394032754503754132161405686935...
		

Links

• Tengiz O. Gogoberidze, Baker's dozen digits of two sums involving reciprocal products of an integer and its greatest prime factor, arXiv:2407.12047 [math.GM], 2024, Table 2, s=2.

Crossrefs

Cf. A085548 (P(2)), A136271 (P'(2)).

Programs

Mathematica

$MaxExtraPrecision = 200; RealDigits[N[PrimeZetaP''[2], 120]][[1]] (* Amiram Eldar, Aug 19 2024 *)

Formula

Equals Sum_{primes = 2,3,5,7,...} log(p)^2/p^2.

Extensions

More terms from Amiram Eldar, Aug 19 2024