A271742 Decimal expansion of Hardy-Littlewood constant C_7 = Product_{p prime > 7} 1/(1-1/p)^7 (1-7/p).

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

Offset: 0

Author

Jean-François Alcover, Apr 17 2016

Keywords

• nonn
• cons

Examples

			0.3694375103864986893231907498767507770553729138930318252910123...
		

References

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

Links

• B. H. Mayoh, The 2nd Goldbach conjecture revisited, BIT 8 (1968) 128-133 Table 5.

Crossrefs

Cf. A005597, A065418, A065419, A269843, A269846.

Programs

Mathematica

$MaxExtraPrecision = 1100; digits = 99; terms = 1000; P[n_] := PrimeZetaP[ n] - 1/2^n - 1/3^n - 1/5^n - 1/7^n; LR = Join[{0, 0}, LinearRecurrence[ {8, -7}, {-42, -336}, 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

PARI

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