A382603 Decimal expansion of Sum_{p prime} 1/((p - 1)*p^3*(p + 1)^3).

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

Offset

0,3

Links

Table of n, a(n) for n=0..94.

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

Formula

Equals 2*A085548 - A085541 + A136141/8 - 31*A179119/8 + 7*A382554/4 + A382555/2.

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

Example

0.0049292506577307662291367679165558750524552...

Prog

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

Crossrefs

Cf. A085541, A085548, A136141, A179119, A382554, A382555.

Sequence in context: A397025 A277526 A196505 * A203816 A070437 A238324

Adjacent sequences: A382600 A382601 A382602 * A382604 A382605 A382606

Keyword

nonn,cons

Author

Artur Jasinski, Mar 31 2025

Status

approved