A340213 Decimal expansion of the constant kappa(-5) = (1/2)*sqrt(sqrt(5)*log(9+4*sqrt(5))/(3*Pi))*sqrt(A340794*A340665).

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

Offset

0,1

Comments

For general definition of the constants kappa(n) see Steven Finch 2009 p. 7, for this particular case kappa(-5) see p. 11.

Links

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

Steven Finch, Quartic and Octic Characters Modulo n, arXiv:0907.4894 [math.NT], 2009 p. 7-11.

Formula

Equals exp(-gamma/2)*log((1+sqrt(5))/2)*sqrt(5/Pi)/(2*C(5,2)*C(5,3)), where C(5,2) and C(5,3) are Mertens constants see A340839.

Equals 2*A340866*exp(gamma/4)*((1/5)*log((1+sqrt(5))/2))^(3/4)/sqrt(A340004).

Equals 2*A340866*exp(gamma/4)*log((1+sqrt(5))/2)/(sqrt(5*Pi)*A340884^(1/4)).

Equals 2*A340839*A340866*exp(gamma/2)*log((1+sqrt(5))/2)/sqrt(5*Pi).

Equals sqrt((1/3)*Pi*log(9+4*sqrt(5)))/(sqrt(5^(3/2)*A340004*A340127)). [Finch 2009 p. 11]

Example

0.51593948227965348495312501394...

Crossrefs

Cf. A340004, A340127, A340665, A340794, A340839, A340866.

Sequence in context: A103986 A196404 A128359 * A170903 A319663 A255166

Adjacent sequences: A340210 A340211 A340212 * A340214 A340215 A340216

Keyword

nonn,cons

Author

Artur Jasinski, Jan 26 2021

Status

approved