A269843 Decimal expansion of Hardy-Littlewood constant C_5 = Product_{p prime > 5} 1/(1-1/p)^5 (1-5/p).

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

Offset

0,1

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

0.4098748850882364744787812123379552778963580132549454698263363988...

Mathematica

$MaxExtraPrecision = 800; digits = 99; terms = 800; P[n_] := PrimeZetaP[n] - 1/2^n - 1/3^n - 1/5^n; LR = Join[{0, 0}, LinearRecurrence[{6, -5}, {-20, -120}, 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)^5*(1-5/p), 1, 7) \\ Amiram Eldar, Mar 11 2021

Crossrefs

Cf. A005597, A065418, A065419, A001692.

Sequence in context: A187286 A187189 A021248 * A247127 A277896 A376732

Adjacent sequences: A269840 A269841 A269842 * A269844 A269845 A269846

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 17 2016

Status

approved