A065468 Decimal expansion of Product_{p prime} (1 - 1/(p^5*(p+1))).

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

Offset

0,1

Links

Table of n, a(n) for n=0..97.

R. J. Mathar, Hardy-Littlewood constants embedded into..., arXiv:0903.2514 [math.NT], 2009-2011, Table 5, constant Q_1^(5).

G. Niklasch, Some number theoretical constants: 1000-digit values. [Cached copy]

Example

0.9885043977412469087511066238511866644...

Mathematica

$MaxExtraPrecision = 500; digits = 98; terms = 500; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0, 0, 0, 0}, LinearRecurrence[{-2, -1, 0, 0, 0, 1, 1}, {-6, 7, -8, 9, -10, 11, -18}, terms + 10]]; r[n_Integer] := LR[[n]]; Exp[ NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Apr 18 2016 *)

Prog

(PARI) prodeulerrat(1 - 1/(p^5*(p+1))) \\ Amiram Eldar, Mar 13 2021

Crossrefs

Cf. A078083.

Sequence in context: A021507 A256254 A203078 * A258752 A363704 A195477

Adjacent sequences: A065465 A065466 A065467 * A065469 A065470 A065471

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 19 2001

Status

approved