A131224 Continued fraction expansion of 2*Pi/log(2).

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, 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, 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

Offset: 0

Author

Jonathan Sondow, Jun 19 2007

Keywords

• cofr
• nonn

Comments

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).

Examples

			9.0647202836543... = A019692 / A002162.
		

References

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

Links

• J. Sondow, Zeros of the alternating zeta function on the line R(s)=1, arXiv:math/0209393 [math.NT], 2002-2003.
• J. Sondow, Zeros of the alternating zeta function on the line R(s)=1, Amer. Math. Monthly 110 (2003) 435-437.
• J. Sondow, A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis, arXiv:0706.2840 [math.NT], 2007-2010.
• J. Sondow, A Simple Counterexample to Havil's "Reformulation" of the Riemann Hypothesis, Elemente der Mathematik 67 (2012), pp. 61-67.

Crossrefs

Cf. A131223 (decimal expansion).

Programs

Mathematica

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

Extensions

Offset changed by Andrew Howroyd, Aug 03 2024