A382578 - OEIS

A382578

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

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

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..81.

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

FORMULA

Equals A085548 - 3*A179119 + 2*A382554 + A382555.

Equals Sum_{k>=5} (-1)^(k+1) * ((k-4)(k-3)/2) * P(k), where P is the prime zeta function. - Amiram Eldar, Apr 02 2025

EXAMPLE

0.01122854604877876221255494209480691223552713354689...

PROG

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

CROSSREFS

Cf. A085548, A179119, A382554, A382555.

Sequence in context: A021818 A388232 A336198 * A241328 A223041 A024558

Adjacent sequences: A382575 A382576 A382577 * A382579 A382580 A382581

KEYWORD

nonn,cons

AUTHOR

Artur Jasinski, Mar 31 2025

STATUS

approved