A272531 - OEIS

%I #11 Jan 17 2020 16:29:31

%S 1,1,8,7,3,0,9,3,4,9,5,7,6,4,0,8,4,3,0,1,7,6,6,6,8,8,4,1,1,5,5,3,3,8,

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

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

%N Decimal expansion of C_2 (so named by S. Finch), a constant which is an analog of Niven's constant when mean of exponents is considered instead of maximum.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.2 Meissel-Mertens constants (pp. 94-95) and Section 2.6 Niven's constant p.112.

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 15.

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>

%F C_2 = C_1 (1 - M) - N, using Finch's notation, where C_1 is A136141, M A077761 and N A085548.

%e 0.1187309349576408430176668841155338623125786669962548878395960878789...

%t digits = 100;

%t C1 = NSum[PrimeZetaP[n], {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits] ;

%t M = EulerGamma - NSum[PrimeZetaP[n]/n, {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 3*digits] ;

%t N0 = PrimeZetaP[2];

%t C2 = C1 (1 - M) - N0;

%t RealDigits[C2, 10, digits][[1]]

%Y Cf. A033150, A077761, A085548, A136141.

%K nonn,cons

%O 0,3

%A _Jean-François Alcover_, May 02 2016