A382580 Decimal expansion of Sum_{p prime} 1/((p - 1)*(p + 1)^3).

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

Offset: 0

Author

Artur Jasinski, Mar 31 2025

Keywords

• nonn
• cons

Examples

			0.046445850131533282948246363741952490263368309214120992009572611741379098614202478270928...
		

Links

• Index to constants which are prime zeta sums {0,1,3}.

Crossrefs

Cf. A136141, A179119, A382554, A382555.

Programs

PARI

sumeulerrat(1/((p-1)*(p+1)^3)) \\ Amiram Eldar, Apr 02 2025

Formula

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

Equals Sum_{k>=2} (k-1)^2 * P(2*k) - (k-1)*k * P(2*k+1), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025