cp's OEIS Frontend

A272531 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.

%I A272531 #12 Feb 16 2025 08:33:34
%S A272531 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 A272531 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 A272531 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 A272531 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 A272531 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 A272531 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 15.
%H A272531 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>
%F A272531 C_2 = C_1 (1 - M) - N, using Finch's notation, where C_1 is A136141, M A077761 and N A085548.
%e A272531 0.1187309349576408430176668841155338623125786669962548878395960878789...
%t A272531 digits = 100;
%t A272531 C1 = NSum[PrimeZetaP[n], {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 2*digits] ;
%t A272531 M = EulerGamma - NSum[PrimeZetaP[n]/n, {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 3*digits] ;
%t A272531 N0 = PrimeZetaP[2];
%t A272531 C2 = C1 (1 - M) - N0;
%t A272531 RealDigits[C2, 10, digits][[1]]
%Y A272531 Cf. A033150, A077761, A085548, A136141.
%K A272531 nonn,cons
%O A272531 0,3
%A A272531 _Jean-François Alcover_, May 02 2016