A065419 Decimal expansion of Hardy-Littlewood constant Product_{p prime >= 5} (1-(6*p^2-4*p+1)/(p-1)^4).

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

Offset

0,1

Comments

For comparison: Product_{n>=5} (1-(6n^2-4n+1)/(n-1)^4) = 3/32. - R. J. Mathar, Feb 25 2009

Links

Table of n, a(n) for n=0..98.

R. J. Mathar, Hardy-Littlewood constants embedded into infinite products over all positive integers, arXiv:0903.2514 [math.NT], 2009-2011, constant C_1^(4).

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

Example

0.30749487875832709312335448607107685302...

Mathematica

$MaxExtraPrecision = 1000; digits = 99; terms = 1000; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n; LR = Join[{0, 0}, LinearRecurrence[{5, -4}, {-12, -60}, 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 17 2016 *)

Prog

(PARI) prodeulerrat(1-(6*p^2-4*p+1)/(p-1)^4, 1, 5) \\ Amiram Eldar, Mar 10 2021

Crossrefs

Cf. A065418, A027377, A065431.

Sequence in context: A369094 A322018 A200339 * A019092 A115870 A115860

Adjacent sequences: A065416 A065417 A065418 * A065420 A065421 A065422

Keyword

cons,nonn

Author

N. J. A. Sloane, Nov 15 2001

Extensions

A sign in the definition corrected by R. J. Mathar, Feb 25 2009

Status

approved