OFFSET
1,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 85.
FORMULA
D = (9/2) Product_{p prime > 3} p^2(p-3)/(p-1)^3.
EXAMPLE
2.8582485957192204324301346607263508780392955929956760290488...
MATHEMATICA
$MaxExtraPrecision = 800; digits = 96; terms = 1000; P[n_] := PrimeZetaP[n] - 1/2^n - 1/3^n; LR = Join[{0, 0}, LinearRecurrence[{4, -3}, {-6, -24}, terms + 10]]; r[n_Integer] := LR[[n]]; (9/2)*Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
PROG
(PARI) (9/2) * prodeulerrat(p^2*(p-3)/(p-1)^3, 1, 5) \\ Amiram Eldar, Mar 11 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Apr 16 2016
STATUS
approved