A088539 Decimal expansion of (4K/Pi)^2 where K is the Landau-Ramanujan constant.

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

Offset

0,1

References

S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 100

Links

Table of n, a(n) for n=0..103.

W. Bosma and P. Stevenhagen, Density computations for real quadratic units, Math. comp. 65 (1996), 1327-1337; MR 96j : 11171.

Formula

Equals prod(1-1/p^2) where p runs through the primes p==1 mod 4

A088539 * A243379 = 8 / Pi^2. - Vaclav Kotesovec, Apr 30 2020

Equals 1/A175647. - Vaclav Kotesovec, May 05 2020

Example

0.9468064071800793342160944131097562332500695...

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]; (4*LandauRamanujanK/Pi)^2 // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Mar 04 2013, updated Mar 14 2018 *)

Crossrefs

Cf. A002144, A064533, A243379, A243380. Square of A244659.

Sequence in context: A309610 A198989 A255013 * A245084 A199054 A131109

Adjacent sequences: A088536 A088537 A088538 * A088540 A088541 A088542

Keyword

cons,nonn

Author

Benoit Cloitre, Nov 16 2003

Status

approved