A243376 Decimal expansion of 2*K/Pi, a constant related to the asymptotic evaluation of the number of positive integers all of whose prime factors are congruent to 3 modulo 4, where K is the Landau-Ramanujan constant.

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

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..100.

Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See page 5.

Eric Weisstein's MathWorld, Ramanujan constant

Formula

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

Example

0.4865198883858909971272456405868234...

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

Crossrefs

Cf. A064533.

Sequence in context: A296488 A199294 A155741 * A200411 A198885 A336275

Adjacent sequences: A243373 A243374 A243375 * A243377 A243378 A243379

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved