A382579 Decimal expansion of Sum_{p prime} 1/(p^3*(p + 1)^3).

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

Offset

0,3

Links

Table of n, a(n) for n=0..102.

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

Formula

Equals -3*A085548 + A085541 + 6*A179119 - 3*A382554 - A382555.

Equals Sum_{k>=6} (-1)^k * ((k-5)(k-4)/2) * P(k), where P is the prime zeta function. - Amiram Eldar, Apr 01 2025

Example

0.00525172780455019329080703581928723468882690814291812210038301...

Prog

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

Crossrefs

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

Sequence in context: A008566 A111129 A168464 * A059688 A072996 A397630

Adjacent sequences: A382576 A382577 A382578 * A382580 A382581 A382582

Keyword

nonn,cons

Author

Artur Jasinski, Mar 31 2025

Status

approved