A369632 Decimal expansion of Sum_{primes p} 1/(p*(p^2 - 1)).

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

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Formula

Equals Sum_{i>=1} 1/A127917(i) = (A136141 - A179119)/2.

Equals Sum_{k>=1} P(2*k+1), where P(s) is the prime zeta function. - Amiram Eldar, Jan 28 2024

Example

0.22146337139279594342463643588459881748724095830455...

Mathematica

RealDigits[NSum[PrimeZetaP[2*k + 1], {k, 1, Infinity}, WorkingPrecision -> 100]][[1]] (* Amiram Eldar, Jan 28 2024 *)

Prog

(PARI) sumeulerrat(1/(p*(p^2-1))) \\ Amiram Eldar, Jan 28 2024

Crossrefs

Cf. A127917, A136141, A179119.

Sequence in context: A112307 A228336 A111062 * A363493 A193597 A191490

Adjacent sequences: A369629 A369630 A369631 * A369633 A369634 A369635

Keyword

nonn,cons

Author

R. J. Mathar, Jan 28 2024

Extensions

More terms from Amiram Eldar, Jan 28 2024

Status

approved