A219705 Decimal expansion of cos(log(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

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 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

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