

A219705


Decimal expansion of cos(log(2)).


2



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, 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, 2, 7, 1, 2, 9, 5
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OFFSET

0,1


COMMENTS

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


REFERENCES

W. Michael Kelley, The Humongous Book of Calculus Problems. New York: Alpha Books (Penguin Group) p. 233, Problem 15.22.


LINKS

Table of n, a(n) for n=0..104.
Paul J. Nahin, An Imaginary Tale: The Story of sqrt(1), Princeton, New Jersey: Princeton University Press (1988), 143  144.
Elizabeth Volz, An English translation of portions of seven correspondences between Euler and Goldbach on Eulerâ€™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


FORMULA

cos(log(2)) = (2^i + 2^(i))/2.


EXAMPLE

0.76923890136...


MATHEMATICA

RealDigits[Cos[Log[2]], 10, 105][[1]]


PROG

(PARI) cos(log(2)) \\ Charles R Greathouse IV, Nov 25 2012
(Maxima) fpprec:110; ev(bfloat(cos(log(2)))); /* Bruno Berselli, Dec 31 2012 */


CROSSREFS

Cf. A002162, A021017, A220085 (imaginary part of 2^i).
Sequence in context: A011220 A198605 A021017 * A273066 A257964 A178816
Adjacent sequences: A219702 A219703 A219704 * A219706 A219707 A219708


KEYWORD

nonn,cons


AUTHOR

Alonso del Arte, Nov 25 2012


EXTENSIONS

a(43) ff. corrected by Georg Fischer, Apr 03 2020


STATUS

approved



