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

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, 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, 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

Offset: 1

Author

Jonathan Sondow, Jun 19 2007

Keywords

• cons
• 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).

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

Examples

			9.0647202836543...
		

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. A000796 = Pi, A002162 = log(2), A019692 = 2*Pi, A131224, A163973 = Pi/log(2).

Programs

Mathematica

RealDigits[ N[ 2*Pi/Log[2], 105]] [[1]]

PARI

2*Pi/log(2) \\ Charles R Greathouse IV, Aug 19 2015