cp's OEIS Frontend

A131223 Decimal expansion of 2*Pi/log(2).

%I A131223 #25 Jun 04 2019 06:22:42
%S A131223 9,0,6,4,7,2,0,2,8,3,6,5,4,3,8,7,6,1,9,2,5,5,3,6,5,8,9,1,4,3,3,3,3,3,
%T A131223 6,2,0,3,4,3,7,2,2,9,3,5,4,4,7,5,9,1,1,6,8,3,7,2,0,3,3,0,9,5,8,8,1,2,
%U A131223 0,1,9,0,7,4,4,2,6,1,0,2,0,4,5,1,8,1,6,7,7,5,9,2,0,8,0,3,2,1,7,9,3,0,6,1
%N A131223 Decimal expansion of 2*Pi/log(2).
%C A131223 Imaginary part of the first complex zero of the alternating zeta function. The pair a=1, b=2*Pi/log(2) is a counterexample to the incorrect reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant. See Sondow (2012).
%C A131223 Also the Bekenstein bound in natural (Planck) units: the information (in bits) contained in a system with mass m and radius r is at most this constant times m*r. - _Charles R Greathouse IV_, Aug 19 2015
%D A131223 J. Havil, Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003, p. 207.
%H A131223 J. Sondow, <a href="https://arxiv.org/abs/math/0209393">Zeros of the alternating zeta function on the line R(s)=1</a>, arXiv:math/0209393 [math.NT], 2002-2003.
%H A131223 J. Sondow, <a href="https://www.jstor.org/stable/3647831">Zeros of the alternating zeta function on the line R(s)=1</a>, Amer. Math. Monthly 110 (2003) 435-437.
%H A131223 J. Sondow, <a href="https://arxiv.org/abs/0706.2840">A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis</a>, arXiv:0706.2840 [math.NT], 2007-2010.
%H A131223 J. Sondow, <a href="https://doi.org/10.4171/EM/195">A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis</a>, Elemente der Mathematik 67 (2012), pp. 61-67.
%e A131223 9.0647202836543...
%t A131223 RealDigits[ N[ 2*Pi/Log[2], 105]] [[1]]
%o A131223 (PARI) 2*Pi/log(2) \\ _Charles R Greathouse IV_, Aug 19 2015
%Y A131223 Cf. A000796 = Pi, A002162 = log(2), A019692 = 2*Pi, A131224, A163973 = Pi/log(2).
%K A131223 cons,nonn
%O A131223 1,1
%A A131223 _Jonathan Sondow_, Jun 19 2007