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
Examples
0.4865198883858909971272456405868234...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 100.
Links
- 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
Crossrefs
Cf. A064533.
Programs
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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 *)
Formula
2*K/Pi, where K is the Landau-Ramanujan constant (A064533).