A243371 Decimal expansion of 6*K/Pi^2, a constant related to the asymptotic evaluation of the number of positive squarefree integers of the form a^2 + b^2, where K is the Landau-Ramanujan constant.

4, 6, 4, 5, 9, 2, 2, 7, 0, 8, 9, 4, 7, 9, 0, 5, 1, 2, 9, 2, 0, 7, 6, 7, 4, 9, 3, 2, 0, 0, 8, 3, 6, 9, 1, 9, 4, 8, 0, 0, 4, 9, 3, 7, 0, 4, 2, 7, 9, 8, 6, 9, 5, 2, 2, 9, 8, 6, 0, 3, 1, 1, 1, 6, 1, 5, 2, 4, 1, 7, 7, 9, 6, 2, 6, 7, 2, 9, 2, 7, 4, 1, 9, 3, 3, 1, 7, 2, 1, 0, 8, 2, 0, 5, 6, 7, 8, 4, 1

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.

Links

Table of n, a(n) for n=0..98.

Eric Weisstein's MathWorld, Ramanujan constant

Formula

6*K/Pi^2, where K is the Landau-Ramanujan constant.

Example

0.46459227089479051292076749320083691948...

Mathematica

digits = 99; 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]; 6*LandauRamanujanK/Pi^2 // RealDigits[#, 10, digits]& // First (* updated Mar 14 2018 *)

Crossrefs

Cf. A064533.

Sequence in context: A137429 A132024 A092039 * A123999 A014110 A266491

Adjacent sequences: A243368 A243369 A243370 * A243372 A243373 A243374

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved