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A219705
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Decimal expansion of cos(log(2)).
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2
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7, 6, 9, 2, 3, 8, 9, 0, 1, 3, 6, 3, 9, 7, 2, 1, 2, 6, 5, 7, 8, 3, 2, 9, 9, 9, 3, 6, 6, 1, 2, 7, 0, 7, 0, 1, 4, 4, 0, 8, 9, 5, 9, 4, 9, 1, 1, 9, 6, 3, 8, 5, 3, 1, 6, 9, 8, 7, 1, 5, 0, 7, 4, 2, 9, 0, 8, 1, 3, 4, 6, 8, 0, 7, 3, 4, 0, 7, 8, 9, 0, 5, 9, 7, 8, 9, 7, 4, 2, 4, 2, 6, 0, 1, 6, 8, 0, 7
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OFFSET
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0,1
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COMMENTS
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In a letter to Christian Goldbach dated December 9, 1741, Leonhard Euler gave 10/13 as a rational approximation of this number.
Also, real part of 2^i. - Bruno Berselli, Dec 31 2012
The imaginary part of 2^i is A220085. - Robert G. Wilson v, Feb 04 2013
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REFERENCES
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W. Michael Kelley, The Humongous Book of Calculus Problems. New York: Alpha Books (Penguin Group) p. 233, Problem 15.22.
Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton, New Jersey: Princeton University Press (1988): 143 - 144.
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LINKS
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Table of n, a(n) for n=0..97.
Elizabeth Volz, An English translation of portions of seven correspondences between Euler and Goldbach on Euler’s complex exponential paradox and special values of cosine, 2008
Elizabeth Volz and Hieu D. Nguyen, Euler, Goldbach and exact values of trigonometric functions, 2008 preprint
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FORMULA
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cos(log(2)) = (2^i + 2^(-i))/2.
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EXAMPLE
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0.76923890136...
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MATHEMATICA
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RealDigits[Cos[Log[2]], 10, 105][[1]]
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PROG
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(PARI) cos(log(2)) \\ Charles R Greathouse IV, Nov 25 2012
(Maxima) fpprec:110; ev(bfloat(cos(log(2)))); /* Bruno Berselli, Dec 31 2012 */
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CROSSREFS
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Cf. A002162, A021017, A220085 (imaginary part of 2^i).
Sequence in context: A011220 A198605 A021017 * A257964 A178816 A200106
Adjacent sequences: A219702 A219703 A219704 * A219706 A219707 A219708
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KEYWORD
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nonn,cons
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AUTHOR
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Alonso del Arte, Nov 25 2012
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STATUS
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approved
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