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 A019913 #42 Aug 31 2025 12:16:31
%S A019913 2,6,7,9,4,9,1,9,2,4,3,1,1,2,2,7,0,6,4,7,2,5,5,3,6,5,8,4,9,4,1,2,7,6,
%T A019913 3,3,0,5,7,1,9,4,7,4,6,1,8,9,6,1,9,3,7,1,9,4,4,1,9,3,0,2,0,5,4,8,0,6,
%U A019913 6,9,8,3,0,9,1,1,9,9,9,6,2,9,1,8,8,5,3,8,1,3,2,4,2,7,5,1,4,2,4
%N A019913 Decimal expansion of tangent of 15 degrees.
%C A019913 Also, 2 - sqrt(3) = cotangent of 75 degrees. An equivalent definition of this sequence: decimal expansion of x < 1 satisfying x^2 - 4*x + 1 = 0. - _Arkadiusz Wesolowski_, Nov 29 2011
%C A019913 Multiplied by -1 (that is, -2 + sqrt(3)), this is one of three real solutions to x^3 = 15x + 4. The other two are 4 and -2 - sqrt(3), all of which can be found with Viete's formula. - _Alonso del Arte_, Dec 15 2012
%C A019913 Wentworth (1903) shows how to compute the tangent of 15 degrees to five decimal places by the laborious process of adding up the first few terms of Pi/12 + Pi^3/5184 + 2Pi^5/3732480 + 17Pi^7/11287019520 + ... - _Alonso del Arte_, Mar 13 2015
%C A019913 A quadratic integer. - _Charles R Greathouse IV_, Aug 27 2017
%C A019913 This is the radius of the largest sphere that can be placed in the space between a sphere of radius 1 and the corners of its circumscribing cube. - _Amiram Eldar_, Jul 11 2020
%D A019913 Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1). Princeton, New Jersey: Princeton University Press (1988): 22 - 23.
%H A019913 Ivan Panchenko, <a href="/A019913/b019913.txt">Table of n, a(n) for n = 0..1000</a>
%H A019913 Willis F. Kern and James R. Bland, <a href="https://archive.org/details/in.ernet.dli.2015.205959/page/n99/mode/2up">Solid Mensuration: With Proofs</a>, 2nd ed., J. Wiley & Sons, Inc., New York, 1938. See pp. 91-92.
%H A019913 George Albert Wentworth, <a href="https://archive.org/details/newplanespherica00went/page/240/mode/2up">New Plane and Spherical Trigonometry, Surveying, and Navigation</a>, Boston: The Atheneum Press (1903), p. 240.
%H A019913 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.
%H A019913 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A019913 Equals Sum_{k>=1} binomial(2*k,k)/(6^k*(k+1)). - _Amiram Eldar_, Jul 11 2020
%F A019913 Equals exp(-arccosh(2)). - _Amiram Eldar_, Jul 06 2023
%F A019913 tan(Pi/12) = A019824 / A019884. - _R. J. Mathar_, Aug 31 2025
%e A019913 0.2679491924311227064725536...
%t A019913 RealDigits[N[Tan[15 Degree], 200]][[1]] (* _Arkadiusz Wesolowski_, Nov 29 2011 *)
%o A019913 (PARI) 2-sqrt(3) \\ _Charles R Greathouse IV_, Aug 27 2017
%Y A019913 Cf. A002194 (sqrt(3)).
%K A019913 nonn,cons,changed
%O A019913 0,1
%A A019913 _N. J. A. Sloane_