cp's OEIS Frontend

A368645 Decimal expansion of the Mertens constant M(4,1) arising in the formula for the sum of reciprocals of primes p == 1 (mod 4) (negated).

%I A368645 #10 Sep 27 2024 08:04:58
%S A368645 2,8,6,7,4,2,0,5,6,2,2,6,1,7,5,1,9,8,6,5,3,9,4,5,1,4,1,4,3,9,4,2,3,8,
%T A368645 5,7,3,6,4,2,0,4,3,6,6,2,4,6,9,3,8,9,2,0,9,5,7,9,7,8,1,8,2,4,6,0,1,4,
%U A368645 9,1,6,6,1,8,7,2,5,7,9,5,0,4,5,5,3,7,8,4,9,9,7,9,7,7,7,8,3,4,7,1,8,8,9,2,7
%N A368645 Decimal expansion of the Mertens constant M(4,1) arising in the formula for the sum of reciprocals of primes p == 1 (mod 4) (negated).
%C A368645 Data were taken from Languasco and Zaccagnini's web site.
%D A368645 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 95.
%D A368645 Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 205.
%H A368645 Alessandro Languasco and Alessandro Zaccagnini, <a href="https://doi.org/10.1080/10586458.2010.10390624">Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions</a>, Experimental Mathematics, Vol. 19, No. 3 (2010), pp. 279-284; <a href="https://arxiv.org/abs/0906.2132">arXiv preprint</a>, arXiv:0906.2132 [math.NT], 2009.
%H A368645 Alessandro Languasco and Alessandro Zaccagnini, <a href="https://www.dei.unipd.it/~languasco/Mertens-comput.html">Computation of the Mertens and Meissel-Mertens constants for sums over arithmetic progressions</a>.
%F A368645 Equals A368646 - A086239.
%F A368645 Equals lim_{x->oo} (Sum_{primes p == 1 (mod 4), p <= x} 1/p - log(log(x))/2).
%F A368645 Equals gamma/2 - log(4*K_1/sqrt(Pi)) + Sum_{prime p == 1 (mod 4)} (log(1-1/p) + 1/p), where gamma is Euler's constant (A001620) and K_1 is Landau-Ramanujan constant (A064533).
%e A368645 -0.28674205622617519865394514143942385736420436624693...
%Y A368645 Cf. A001620, A002144, A064533, A077761, A086239, A161529, A368644, A368646.
%K A368645 nonn,cons
%O A368645 0,1
%A A368645 _Amiram Eldar_, Jan 02 2024