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A243379 Decimal expansion of 1/(2*K^2) = prod_(p prime congruent to 3 modulo 4) (1 - 1/p^2), where K is the Landau-Ramanujan constant. 0
8, 5, 6, 1, 0, 8, 9, 8, 1, 7, 2, 1, 8, 9, 3, 4, 7, 6, 9, 0, 6, 0, 3, 3, 0, 0, 6, 1, 4, 8, 0, 6, 1, 1, 7, 3, 4, 8, 1, 0, 7, 8, 4, 2, 7, 3, 8, 8, 1, 7, 3, 4, 9, 0, 8, 6, 0, 5, 1, 8, 4, 0, 0, 5, 8, 3, 4, 3, 0, 7, 9, 6, 1, 1, 1, 8, 6, 3, 6, 5, 8, 9, 6, 2, 3, 3, 8, 1, 2, 9, 4, 5, 1, 7, 7, 7, 7, 0, 9, 7, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals 1/1.168075586.., where 1.168.. is zeta_(m=4,n=3)(s=2) in the table of Section 3.3 of arxiv:1008.2547. - R. J. Mathar, Nov 14 2014

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.

LINKS

Table of n, a(n) for n=0..100.

Richard J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], (15-August-2010)

Eric Weisstein's MathWorld, Ramanujan constant

FORMULA

1/(2*K^2), where K is the Landau-Ramanujan constant (A064533).

EXAMPLE

0.856108981721893476906033006148061173481...

MATHEMATICA

digits = 101; LandauRamanujanK = 1/Sqrt[2]*NProduct[((1 - 2^(-2^n))*Zeta[2^n]/DirichletBeta[2^n])^(1/2^(n + 1)), {n, 1, 24}, WorkingPrecision -> digits + 5]; 1/(2*LandauRamanujanK^2) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)

CROSSREFS

Cf. A064533.

Sequence in context: A201295 A011107 A318335 * A214174 A154433 A107828

Adjacent sequences:  A243376 A243377 A243378 * A243380 A243381 A243382

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Jun 04 2014

STATUS

approved

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Last modified May 25 19:44 EDT 2019. Contains 323576 sequences. (Running on oeis4.)