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A088539 Decimal expansion of (4K/Pi)^2 where K is the Landau-Ramanujan constant. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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-Fran├žois Alcover, Mar 04 2013, updated Mar 14 2018 *)

CROSSREFS

Cf. A064533. 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

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Last modified October 18 22:03 EDT 2019. Contains 328211 sequences. (Running on oeis4.)