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, 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

Table of n, a(n) for n=1..99.

Eric Weisstein's MathWorld, Goldbach Conjecture.

Eric Weisstein's MathWorld, Vinogradov's theorem.

Wikipedia, Goldbach's conjecture.

Wikipedia, 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

Adjacent sequences: A271948 A271949 A271950 * A271952 A271953 A271954

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 17 2016

Status

approved