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A271951
Decimal expansion of (1/2) Product_{p prime} 1+1/(p-1)^3, a constant related to I. M. Vinogradov's proof of the "ternary" Goldbach conjecture.
1
1, 1, 5, 0, 4, 8, 0, 7, 7, 2, 3, 5, 6, 6, 1, 8, 5, 2, 7, 2, 7, 8, 4, 8, 8, 0, 7, 4, 3, 7, 4, 6, 9, 8, 0, 9, 0, 6, 3, 0, 3, 9, 3, 2, 9, 8, 5, 1, 1, 0, 8, 3, 6, 8, 0, 6, 8, 8, 1, 9, 3, 0, 5, 9, 0, 2, 2, 8, 2, 6, 3, 2, 3, 2, 5, 4, 3, 8, 0, 1, 3, 7, 1, 5, 7, 4, 0, 5, 2, 0, 9, 2, 9, 9, 4, 3, 6, 3, 8
OFFSET
1,3
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.1 Hardy-Littlewood Constants, p. 88.
LINKS
Eric Weisstein's MathWorld, Goldbach Conjecture.
Eric Weisstein's MathWorld, Vinogradov's theorem.
EXAMPLE
1.150480772356618527278488074374698090630393298511083680688193059...
MATHEMATICA
$MaxExtraPrecision = 1600; digits = 99; terms = 1600; P[n_] := PrimeZetaP[n]; LR = Join[{0, 0, 0}, LinearRecurrence[{4, -6, 3}, {3, 12, 30}, terms + 10]]; r[n_Integer] := LR[[n]]; (1/2) Exp[NSum[r[n]*P[n - 1]/(n - 1), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10]] // RealDigits[#, 10, digits]& // First
PROG
(PARI) (1/2) * prodeulerrat(1+1/(p-1)^3) \\ Amiram Eldar, Mar 14 2021
CROSSREFS
Cf. A005597.
Sequence in context: A309723 A198839 A062521 * A157700 A099645 A220412
KEYWORD
nonn,cons
AUTHOR
STATUS
approved