%I #16 Dec 20 2024 13:13:51

%S 2,3,3,2,5,8,2,2,7,5,7,3,3,2,2,0,8,8,1,7,6,5,8,2,8,7,7,6,0,7,1,0,2,7,

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

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

%N Decimal expansion of constant 1 + B3 (or 1 + B_3) related to the Mertens constant.

%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, pp. 94-98

%H David Broadhurst, <a href="/A238114/b238114.txt">Table of n, a(n) for n = 1..300</a>

%H David Broadhurst, <a href="http://physics.open.ac.uk/~dbroadhu/cert/cohenb3.ps">The Mertens constant ...</a>

%H David Broadhurst, <a href="http://physics.open.ac.uk/~dbroadhu/cert/cohenb3.txt">1000 digits</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MertensConstant.html">Mertens Constant</a>

%F B_3 = lim_{x->oo} ( log x - Sum_{p <= x} log p / p ). - Dick Boland, Mar 09 2008

%e 2.3325822757332208817658287760710277488384594890424226617871308997573400417193...

%t digits = 99;

%t B3 = EulerGamma - NSum[PrimeZetaP'[n], {n, 2, Infinity}, WorkingPrecision -> digits+50, NSumTerms -> 200];

%t RealDigits[1 + B3, 10, digits][[1]] (* _Jean-François Alcover_, Apr 26 2018 *)

%Y Equals 1 + A083343, the latter being the main entry for this constant.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_, Mar 05 2014