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A243379 Decimal expansion of 1/(2*K^2) = Product_(p prime congruent to 3 modulo 4) (1 - 1/p^2), where K is the Landau-Ramanujan constant. 14
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
Richard J. Mathar, Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], 2010-2015.
Eric Weisstein's MathWorld, Ramanujan constant
FORMULA
1/(2*K^2), where K is the Landau-Ramanujan constant (A064533).
A088539 * A243379 = 8 / Pi^2. - Vaclav Kotesovec, Apr 30 2020
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
Sequence in context: A011107 A356805 A318335 * A214174 A366587 A154433
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)