A131224 - OEIS

%I #26 Aug 03 2024 11:53:21

%S 9,15,2,4,1,1,1,1,2,2,3,1,1,1,1,3,4,1,1,1,1,24,1,2,1,1,1,20,1,2,3,6,1,

%T 1,2,49,11,3,4,2,2,2,1,6,1,11,1,1,3,29,16,1,1,5,1,9,2,2,1,17,1,1,1,1,

%U 2,1,9,1,1,11,1,12,2,12,2,2,168,1,5,1,5,1,1,1,1,6,1,2,27,1,1,1,2,1,16,3,9,4

%N Continued fraction expansion of 2*Pi/log(2).

%C 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).

%D J. Havil, Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003, p. 207.

%H 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 J. Sondow, <a href="http://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 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 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 9.0647202836543... = A019692 / A002162.

%t ContinuedFraction[2*Pi/Log[2],105] [[1]]

%Y Cf. A131223 (decimal expansion).

%K cofr,nonn

%O 0,1

%A _Jonathan Sondow_, Jun 19 2007

%E Offset changed by _Andrew Howroyd_, Aug 03 2024