A264736 Decimal expansion of Product_{p prime > 2} 1-1/(p^2-3p+3), a constant related to I. M. Vinogradov's proof of the "ternary" Goldbach conjecture.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 88.

Links

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

Eric Weisstein's MathWorld, Goldbach's Conjecture.

Eric Weisstein's MathWorld, Vinogradov's theorem.

Wikipedia, Goldbach's conjecture.

Wikipedia, Vinogradov's theorem.

Formula

Equals A005597 / A271951.

Example

0.5738138626120705990478863934579063276647761095586873862487...

Mathematica

$MaxExtraPrecision = 600; digits = 99; terms = 600; P[n_] := PrimeZetaP[n] - 1/2^n; LR = LinearRecurrence[{6, -14, 15, -6}, {0, 0, -2, -9}, 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/(p^2-3*p+3), 1, 3) \\ Amiram Eldar, Mar 11 2021

Crossrefs

Cf. A005597, A271951.

Sequence in context: A155529 A261624 A152081 * A200620 A195389 A345653

Adjacent sequences: A264733 A264734 A264735 * A264737 A264738 A264739

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 17 2016

Status

approved