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A131223 Decimal expansion of 2*Pi/ln(2). +0
1
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 (list; cons; graph; listen)
OFFSET

1,1

COMMENT

Imaginary part of the first complex zero of the alternating zeta function. The pair a=1, b=2*Pi/ln(2) is a counterexample to the reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant.

REFERENCES

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

J. Sondow, Zeros of the alternating zeta function on the line R(s)=1, Amer. Math. Monthly 110 (2003) 435-437.

LINKS

J. Sondow, Zeros of the alternating zeta function on the line R(s)=1

J. Sondow, A Counterexample to Havil's "Reformulation" of the Riemann Hypothesis

EXAMPLE

9.0647202836543...

MATHEMATICA

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

CROSSREFS

Cf. A000796 = Pi, A002162 = ln(2), A019692 = 2*Pi.

Sequence in context: A019740 A019874 A068467 this_sequence A093766 A097674 A097669

Adjacent sequences: A131220 A131221 A131222 this_sequence A131224 A131225 A131226

KEYWORD

cons,nonn

AUTHOR

Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Jun 19 2007

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Last modified December 2 15:58 EST 2008. Contains 150992 sequences.


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