A271886 Decimal expansion of the constant D related to the conjectured asymptotic expression of the counting function of prime triples as D*n/log(n)^3.

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

Offset: 1

Author

Jean-François Alcover, Apr 16 2016

Keywords

• nonn
• cons

Examples

			2.8582485957192204324301346607263508780392955929956760290488...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 85.

Crossrefs

Cf. A005597.

Programs

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

PARI

(9/2) * prodeulerrat(p^2*(p-3)/(p-1)^3, 1, 5) \\ Amiram Eldar, Mar 11 2021

Formula

D = (9/2) Product_{p prime > 3} p^2(p-3)/(p-1)^3.