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%I #58 Jan 27 2021 16:22:05
%S 1,2,2,5,2,3,8,4,3,8,5,3,9,0,8,4,5,8,0,0,5,7,6,0,9,7,7,4,7,4,9,2,2,0,
%T 5,2,7,5,4,0,5,9,5,5,0,9,3,9,1,6,4,9,9,3,8,7,6,7,3,3,3,6,4,4,3,0,2,6,
%U 7,3,1,4,2,9,6,4,4,1,7,6,1,9,2,7,3,8,4,1,6,1,9,5,6,2,7,3,6,5,2,9,5,6,6,7,5,6,7,9,6,2,7,9,0,4,2,5,9,6,3,2,4,0,2,1,1,0,0,4,8,0,7,6,8,7,9,3,3,7,6,5,5,0,4,6,7,8,7,4,2,6,0,3,2,5,0,1,1,5,3
%N Decimal expansion of Mertens constant C(5,1).
%C Data taken from Alessandro Languasco and Alessandro Zaccagnini 2007.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.2 Meissel-Mertens constants (pp. 94-95)
%H Vaclav Kotesovec, <a href="/A340839/b340839.txt">Table of n, a(n) for n = 1..499</a>
%H Alessandro Languasco and Alessandro Zaccagnini, <a href="https://doi.org/10.1090/S0025-5718-08-02148-0">On the constant in the Mertens product for arithmetic progressions. II: Numerical values</a>, Math. Comp. 78 (2009), 315-326.
%H Alessandro Languasco and Alessandro Zaccagnini, <a href="https://www.math.unipd.it/~languasc/MCcomput/MCfinalresults.pdf">Computation of the Mertens constants - more than 100 correct digits</a>, (2007), 1-134 (digital data relative to the previous paper). [in this table on page 4, the last correct digit is a(109), beyond the level there certified. - _Vaclav Kotesovec_, Jan 26 2021]
%H Alessandro Languasco and Alessandro Zaccagnini, <a href="https://www.math.unipd.it/~languasc/MCcomput/MertensConstantsfinal.gp">Computation of the Mertens constants mod q; 3 <= q <= 100</a>, (2007) (GP-PARI procedure 100 digits accuracy).
%H Alessandro Languasco and Alessandro Zaccagnini, <a href="https://projecteuclid.org/euclid.facm/1269437065">On the constant in the Mertens product for arithmetic progressions. I. Identities</a>., Funct. Approx. Comment. Math. Volume 42, Number 1 (2010), 17-27.
%H For other links see A340711.
%F A = C(5,1)=1.225238438539084580057609774749220527540595509391649938767...
%F B = C(5,2)=0.546975845411263480238301287430814037751996324100819295153...
%F C = C(5,3)=0.805951040448267864057376860278430932081288114939010897934...
%F D = C(5,4)=1.299364547914977988160840014964265909502574970408329662016...
%F A*B*C*D = 0.70182435445860646228... = (5/4)*exp(-gamma), where gamma is the Euler-Mascheroni constant A001620.
%F Formula from the article by Languasco and Zaccagnini, 2010, p.9:
%F A = ((13*sqrt(5)*Pi^2*exp(-gamma))/(150*log((1+sqrt(5))/2))*A340628/A340808)^(1/4).
%e 1.225238438539084580057609774749220527540595509391649938767...
%Y Cf. A077761, A083343, A091589, A138312, A161529, A230767, A238114, A271971, A340127, A340794, A340866.
%K nonn,cons
%O 1,2
%A _Artur Jasinski_, Jan 23 2021
%E Last 11 digits corrected by _Vaclav Kotesovec_, Jan 25 2021
%E More digits from _Vaclav Kotesovec_, Jan 26 2021
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