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

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, 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, 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

Offset: 0

Author

Jonathan Vos Post, Jun 12 2009

Keywords

• cons
• nonn

Comments

First entry of Table 1, p. 7, of Languasco and Zaccagnini.

Examples

			0.356890479509443129119649567223185895478588864544...
		

Links

• Alessandro Languasco and Alessandro Zaccagnini, Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions, Experimental Mathematics, Vol. 19, No. 3 (2010), pp. 279-284; arXiv preprint, arXiv:0906.2132 [math.NT], 2009.
• Alessandro Languasco and Alessandro Zaccagnini, Computation of the Mertens and Meissel-Mertens constants for sums over arithmetic progressions.

Crossrefs

Cf. A001620, A301429.

Formula

From Amiram Eldar, Jan 02 2022: (Start)

Equals lim_{x->oo} (Sum_{primes p == 1 (mod 3), p <= x} 1/p - log(log(x))/2).

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)

Extensions

More digits from R. J. Mathar, Jul 04 2009