A243375 Decimal expansion of 1/(4*K), a constant related to the asymptotic evaluation of the number of positive integers all of whose prime factors are congruent to 1 modulo 4, where K is the Landau-Ramanujan constant.

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

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..103.

Eric Weisstein's MathWorld, Ramanujan constant

Formula

1/(4*K), where K is the Landau-Ramanujan constant.

Example

0.327129366941026382400232869028392799695...

Mathematica

digits = 104; 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]; 1/(4*LandauRamanujanK) // RealDigits[#, 10, digits] & // First (* updated Mar 18 2018 *)

Crossrefs

Cf. A064533.

Sequence in context: A255820 A318436 A369042 * A369045 A163659 A348337

Adjacent sequences: A243372 A243373 A243374 * A243376 A243377 A243378

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved