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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.
0
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
Eric Weisstein's MathWorld, Goldbach's Conjecture.
Eric Weisstein's MathWorld, 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
Sequence in context: A374003 A261624 A152081 * A200620 A195389 A345653
KEYWORD
nonn,cons
AUTHOR
STATUS
approved