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

0,1

Comments

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

Links

Table of n, a(n) for n=0..104.

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.

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)

Crossrefs

Cf. A001620, A301429.

Sequence in context: A021741 A201906 A267158 * A133043 A094058 A288134

Adjacent sequences: A161526 A161527 A161528 * A161530 A161531 A161532

Keyword

cons,nonn

Author

Jonathan Vos Post, Jun 12 2009

Extensions

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

Status

approved