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A161529
Decimal expansion of negative of constant M(3,1) arising in Mertens and Meissel-Mertens constants for sums over arithmetic progressions.
5
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
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.
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)
EXAMPLE
0.356890479509443129119649567223185895478588864544...
CROSSREFS
Sequence in context: A021741 A201906 A267158 * A133043 A094058 A288134
KEYWORD
cons,nonn
AUTHOR
Jonathan Vos Post, Jun 12 2009
EXTENSIONS
More digits from R. J. Mathar, Jul 04 2009
STATUS
approved