A243377 Decimal expansion of a constant related to the asymptotic evaluation of Product_{p prime congruent to 1 modulo 4} (1 + 1/p).

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.3 Landau-Ramanujan constant, p. 101.

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's World of Mathematics, Ramanujan constant.

Formula

Equals (4/Pi^(3/2))*exp(gamma/2)*K, where gamma is the Euler-Mascheroni constant and K the Landau-Ramanujan constant.

Equals 2/(Pi*A088541) = A060294/A088541. - Amiram Eldar, Nov 16 2021

Example

0.732649819283832613620305823117683687363...

Mathematica

digits = 103; 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/Pi^(3/2)*Exp[EulerGamma/2]*LandauRamanujanK // RealDigits[#, 10, digits] & // First (* updated Mar 14 2018 *)

Crossrefs

Cf. A001620, A060294, A064533, A088541.

Sequence in context: A340485 A309387 A298530 * A245532 A324714 A075564

Adjacent sequences: A243374 A243375 A243376 * A243378 A243379 A243380

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved