A335576 Decimal expansion of Mertens constant C(5,2).

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

Offset

0,1

Comments

First 100 digits from Alessandro Languasco and Alessandro Zaccagnini 2007 p. 4.

Links

Table of n, a(n) for n=0..99.

Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens constants - more than 100 correct digits, (2007), 1-134.

Formula

A = C(5,1)=1.2252384385390845800576097747492205... see A340839.

B = C(5,2)=0.5469758454112634802383012874308140... this constant.

C = C(5,3)=0.8059510404482678640573768602784309... see A336798.

D = C(5,4)=1.2993645479149779881608400149642659... see A340866.

A*B*C*D = 0.70182435445860646228... = (5/4)*exp(-gamma), where gamma is the Euler-Mascheroni constant A001620.

B = sqrt(2)*5^(3/4)*sqrt(A340127)*exp(-gamma)/(4*sqrt(A340004)*A^2*C).

B = 2*A*D*log((1+sqrt(5))/2)/(C*sqrt(5)*A340794*A340665).

B = A*D*log((1+sqrt(5))/2)^2/(C*Pi*A340213^2).

From Vaclav Kotesovec, Jan 27 2021: (Start)

B*C = 5^(1/4) * exp(-gamma/2) * sqrt(log((1+sqrt(5))/2) / (2 * A340665 * A340794)).

A*D = 5^(3/4) * exp(-gamma/2) * sqrt(A340665 * A340794 / (8 * log((1+sqrt(5))/2))).

(End)

Example

0.546975845411263480238301287430814...

Crossrefs

Cf. A001620, A336798, A340004, A340127, A340213, A340665, A340794, A340839, A340866.

Sequence in context: A011502 A347185 A345231 * A270841 A097995 A316670

Adjacent sequences: A335573 A335574 A335575 * A335577 A335578 A335579

Keyword

nonn,cons

Author

Artur Jasinski, Jan 26 2021

Status

approved