A269846 Decimal expansion of Hardy-Littlewood constant C_6 = Product_{p prime > 6} 1/(1-1/p)^6 (1-6/p).

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

Offset

0,2

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 86.

Links

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

Example

0.18661429735835839665692484794418833784007394494558930487172669...

Mathematica

$MaxExtraPrecision = 1600; digits = 99; terms = 1600; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n - 1/5^n; LR = Join[{0, 0}, LinearRecurrence[{7, -6}, {-30, -210}, 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

Prog

(PARI) prodeulerrat(1/(1-1/p)^6*(1-6/p), 1, 7) \\ Amiram Eldar, Mar 11 2021

Crossrefs

Cf. A005597, A065418, A065419, A269843.

Sequence in context: A375193 A010527 A270137 * A316136 A102887 A067970

Adjacent sequences: A269843 A269844 A269845 * A269847 A269848 A269849

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 17 2016

Status

approved