A382589 Decimal expansion of Sum_{p prime} 1/((p - 1)^3*p^3*(p + 1)).

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

Offset: 0

Author

Artur Jasinski, Mar 31 2025

Keywords

• nonn
• cons

Examples

			0.04284668047253445152278596382752684587829787893790...
		

Links

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

Crossrefs

Cf. A085541, A085548, A086242, A136141, A179119, A380840.

Programs

PARI

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

Formula

Equals -2*A085548 - A085541 + 31*A136141/8 - 7*A086242/4 + A380840/2 - A179119/8.

Equals Sum_{k>=4} ((k-3)^2 * P(2*k-1) + (k-3)*(k-2) * P(2*k)), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025