%I #23 Sep 27 2024 08:09:25

%S 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,

%T 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,

%U 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

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

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

%H Alessandro Languasco and Alessandro Zaccagnini, <a href="https://www.dei.unipd.it/~languasco/MCcomput/MCfinalresults.pdf">Computation of the Mertens constants - more than 100 correct digits</a>, (2007), 1-134.

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

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

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

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

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

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

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

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

%F From _Vaclav Kotesovec_, Jan 27 2021: (Start)

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

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

%F (End)

%e 0.546975845411263480238301287430814...

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

%K nonn,cons

%O 0,1

%A _Artur Jasinski_, Jan 26 2021