OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree couples, p. 111.
FORMULA
Equals (Pi^2/12)*A065464.
Equals (1/2) * A065463. - Amiram Eldar, Nov 16 2021
EXAMPLE
0.35222110049958279636830167516331860509429321570854902470711342...
MATHEMATICA
$MaxExtraPrecision = 800; digits = 101; terms = 2000; LR = Join[{0, 0}, LinearRecurrence[{-2, 0, 1}, {-2, 3, -6}, terms + 10]]; r[n_Integer] := LR[[n]]; (1/2)*Exp[NSum[r[n]*(PrimeZetaP[n - 1]/(n - 1)), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"]] // RealDigits[#, 10, digits]& // First
PROG
(PARI) prodeulerrat(1 - 1/(p*(p+1)))/2 \\ Amiram Eldar, Nov 16 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Apr 25 2016
STATUS
approved