cp's OEIS Frontend

A161529 Decimal expansion of negative of constant M(3,1) arising in Mertens and Meissel-Mertens constants for sums over arithmetic progressions.

%I A161529 #24 Sep 28 2024 05:33:41
%S A161529 3,5,6,8,9,0,4,7,9,5,0,9,4,4,3,1,2,9,1,1,9,6,4,9,5,6,7,2,2,3,1,8,5,8,
%T A161529 9,5,4,7,8,5,8,8,8,6,4,5,4,4,0,1,1,8,9,1,0,2,4,7,1,9,9,8,2,2,7,0,0,7,
%U A161529 1,0,5,2,5,6,3,3,5,1,1,7,8,6,0,8,6,8,2,4,3,0,9,2,2,3,4,6,6,2,8,0,9,7,1,5,7
%N A161529 Decimal expansion of negative of constant M(3,1) arising in Mertens and Meissel-Mertens constants for sums over arithmetic progressions.
%C A161529 First entry of Table 1, p. 7, of Languasco and Zaccagnini.
%H A161529 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="http://arxiv.org/abs/0906.2132">arXiv preprint</a>, arXiv:0906.2132 [math.NT], 2009.
%H A161529 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 A161529 From _Amiram Eldar_, Jan 02 2022: (Start)
%F A161529 Equals lim_{x->oo} (Sum_{primes p == 1 (mod 3), p <= x} 1/p - log(log(x))/2).
%F A161529 Equals gamma/2 - log(3*sqrt(3/Pi)*K_3) + Sum_{prime p == 1 (mod 3)} (log(1-1/p) + 1/p), where gamma is Euler's constant (A001620) and K_3 = A301429. (End)
%e A161529 0.356890479509443129119649567223185895478588864544...
%Y A161529 Cf. A001620, A301429.
%K A161529 cons,nonn
%O A161529 0,1
%A A161529 _Jonathan Vos Post_, Jun 12 2009
%E A161529 More digits from _R. J. Mathar_, Jul 04 2009