A382601 Decimal expansion of Sum_{p prime} 1/((p - 1)*p*(p + 1)^3).

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

Offset: 0

Author

Artur Jasinski, Mar 31 2025

Keywords

• nonn
• cons

Examples

			0.02140952451105972173249874583065002197680928629050357743...
		

Links

• Index to constants which are prime zeta sums {1,1,3}.

Crossrefs

Cf. A136141, A179119, A382554, A382555.

Programs

PARI

sumeulerrat(1/((p-1)*p*(p+1)^3)) \\ Amiram Eldar, Apr 01 2025

Formula

Equals A136141/8 - 7*A179119/8 + 3*A382554/4 + A382555/2.

Equals Sum_{k>=3} ((k-2)^2 * P(2*k-1) - (k-2)*(k-1) * P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025