A243381 Decimal expansion of Pi^2/(16*K^2*G) = Product_{p prime congruent to 3 modulo 4} (1 + 1/p^2), where K is the Landau-Ramanujan constant and G Catalan's constant.

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

Offset

1,3

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..2500

Eric Weisstein's MathWorld, Ramanujan constant

Eric Weisstein's MathWorld, Catalan's Constant

Formula

Pi^2/(16*K^2*G), where K is the Landau-Ramanujan constant (A064533) and G Catalan's constant (A006752).

A243380 * A243381 = 12/Pi^2. - Vaclav Kotesovec, Apr 30 2020

Example

1.1530805615854478703652580685617633651...

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]; Pi^2/(16*LandauRamanujanK^2*Catalan) // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

Crossrefs

Cf. A002145, A064533, A243379.

Sequence in context: A200126 A065469 A249522 * A282887 A265729 A181886

Adjacent sequences: A243378 A243379 A243380 * A243382 A243383 A243384

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved