A088541 Decimal expansion of sqrt(Pi)/(2K)*exp(-gamma/2) where K is the Landau-Ramanujan constant and gamma the Euler-Mascheroni constant.

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

Offset

0,1

Comments

An illustration of the Chebyshev effect.

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.

Gareth A. Jones and Alexander K. Zvonkin, A number-theoretic problem concerning pseudo-real Riemann surfaces, arXiv:2401.00270 [math.NT], 2023. See page 6.

S. Uchiyama, On some products involving primes, Proc. Amer. Math. Soc. 28 (1971) 629-630; MR 43#3227.

Formula

sqrt(Pi)/(2K)*exp(-gamma/2) = lim x-->oo prod(1-1/p) where p runs through the primes p==3 mod 4 and p<=x.

Equals A002161*A064533/(2*exp(A155739)). - Michel Marcus, Jun 19 2020

Example

0.868927768234323...

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

Crossrefs

Cf. A002161, A064533, A088540, A155739.

Sequence in context: A191909 A247559 A246768 * A362439 A110214 A305709

Adjacent sequences: A088538 A088539 A088540 * A088542 A088543 A088544

Keyword

cons,nonn

Author

Benoit Cloitre, Nov 16 2003

Status

approved