A243380 Decimal expansion of 192*K^2*G/Pi^4 = Product_{p prime congruent to 1 modulo 4} (1 + 1/p^2), where K is the Landau-Ramanujan constant and G Catalan's constant.

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

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

Equals 192*K^2*G/Pi^4, where K is the Landau-Ramanujan constant (A064533) and G Catalan's constant (A006752).

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

Equals A175647 / 1.001652229636651... both constants from p 26 of arXiv:1008.2537v2. - R. J. Mathar, Aug 21 2022

Example

1.0544399447999484896488194648267179483...

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]; 192*LandauRamanujanK^2*Catalan/Pi^4 // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

Crossrefs

Cf. A002144, A064533, A088539.

Sequence in context: A147533 A241183 A137240 * A244999 A201129 A261509

Adjacent sequences: A243377 A243378 A243379 * A243381 A243382 A243383

Keyword

cons,nonn,changed

Author

Jean-François Alcover, Jun 04 2014

Status

approved