A387289 Decimal expansion of Sum_{n>=1} (-1)^(n+1) P(3*n)/(3*n), where P(x) is the prime zeta function.

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

Offset: 0

Author

Artur Jasinski, Aug 25 2025

Keywords

• nonn
• cons
• new

Examples

			0.055613262596277710178747463453...
		

Crossrefs

Cf. A387293.

Programs

Mathematica

RealDigits[Log[Zeta[3]/Zeta[6]]/3, 10, 105, -1][[1]]

Formula

Equals log(zeta(3)/zeta(6))/3.

Equals log(3*(35*zeta(3))^(1/3)/Pi^2).

Sum_{p prime} Sum_{n>=1} (-1)^(n+1)/p^(3*n)/(3*n) = Sum_{p prime} log((1+1/p^3))/3 = log(Product_{p prime} (1+1/p^3))/3 = log(zeta(3)/zeta(6))/3. - Amiram Eldar, Aug 25 2025