A382573 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*(p + 1)^2).

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

Offset: 0

Author

Artur Jasinski, Mar 31 2025

Keywords

• nonn
• cons

Examples

			0.119441349354286720549913256510757646460932...
		

Links

• Index to constants which are prime zeta sums {0,3,2}.

Crossrefs

Cf. A086242, A136141, A179119, A380840, A382554.

Programs

PARI

sumeulerrat(1/((p-1)^3*(p+1)^2)) \\ Amiram Eldar, Apr 02 2025

Formula

Equals 3*A136141/16 - A086242/4 + A380840/4 + 3*A179119/16 - A382554/8.

Equals Sum_{k>=3} ((k-2)*(k-1)/2) * (P(2*k-1) + P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025