This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219705 #37 Aug 05 2025 13:27:21 %S A219705 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, %T A219705 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, %U A219705 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 %N A219705 Decimal expansion of cos(log(2)). %C A219705 In a letter to Christian Goldbach dated December 9, 1741, Leonhard Euler gave 10/13 as a rational approximation of this number. %C A219705 Also, real part of 2^i. - _Bruno Berselli_, Dec 31 2012 %C A219705 The imaginary part of 2^i is A220085. - _Robert G. Wilson v_, Feb 04 2013 %D A219705 Florian Cajori, A History of Mathematical Notations, Dover edition (2012), par. 309. %D A219705 W. Michael Kelley, The Humongous Book of Calculus Problems. New York: Alpha Books (Penguin Group) p. 233, Problem 15.22. %H A219705 Paul J. Nahin, <a href="http://press.princeton.edu/titles/9259.html">An Imaginary Tale: The Story of sqrt(-1)</a>, Princeton, New Jersey: Princeton University Press (1988), 143 - 144. %H A219705 Elizabeth Volz, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/euler/translations/Euler%20Goldbach%20Letters%20Complex%20Exponential%20Paradox%20English%20Translation.pdf">An English translation of portions of seven correspondences between Euler and Goldbach on Euler’s complex exponential paradox and special values of cosine</a>, 2008 %H A219705 Elizabeth Volz and Hieu D. Nguyen, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/euler/articles/Euler%20Goldbach%20and%20Exact%20Values%20of%20Trigonometric%20Functions.pdf">Euler, Goldbach and exact values of trigonometric functions</a>, 2008 preprint %F A219705 cos(log(2)) = (2^i + 2^(-i))/2. %e A219705 0.76923890136... %t A219705 RealDigits[Cos[Log[2]], 10, 105][[1]] %o A219705 (PARI) cos(log(2)) \\ _Charles R Greathouse IV_, Nov 25 2012 %o A219705 (Maxima) fpprec:110; ev(bfloat(cos(log(2)))); /* _Bruno Berselli_, Dec 31 2012 */ %Y A219705 Cf. A002162, A021017, A220085 (imaginary part of 2^i). %K A219705 nonn,cons %O A219705 0,1 %A A219705 _Alonso del Arte_, Nov 25 2012 %E A219705 a(43) ff. corrected by _Georg Fischer_, Apr 03 2020