A368644 Decimal expansion of the Mertens constant M(3,2) arising in the formula for the sum of reciprocals of primes p == 2 (mod 3).

2, 8, 5, 0, 5, 4, 3, 5, 9, 0, 2, 3, 7, 5, 2, 5, 7, 9, 5, 4, 1, 7, 4, 3, 0, 7, 2, 4, 9, 8, 5, 4, 8, 4, 2, 1, 1, 9, 6, 8, 2, 2, 1, 7, 9, 4, 7, 1, 8, 7, 7, 7, 6, 3, 8, 8, 3, 4, 5, 0, 8, 6, 2, 8, 6, 1, 6, 6, 2, 2, 3, 0, 1, 2, 7, 3, 8, 6, 0, 5, 4, 9, 8, 9, 4, 9, 1, 7, 2, 9, 0, 2, 3, 2, 5, 9, 9, 4, 5, 7, 7, 8, 4, 5, 5

Offset

0,1

Comments

Data were taken from Languasco and Zaccagnini's web site.

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 204.

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

Equals A086241 - A161529.

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

Equals gamma/2 - log(sqrt(Pi/3)/(2*K_3)) + Sum_{prime p == 2 (mod 3)} (log(1-1/p) + 1/p), where gamma is Euler's constant (A001620) and K_3 = A301429.

Example

0.28505435902375257954174307249854842119682217947187...

Crossrefs

Cf. A001620, A003627, A077761, A086241, A161529, A301429, A368645, A368646.

Sequence in context: A054671 A203269 A011058 * A229981 A188731 A188617

Adjacent sequences: A368641 A368642 A368643 * A368645 A368646 A368647

Keyword

nonn,cons

Author

Amiram Eldar, Jan 02 2024

Status

approved