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 A019952 #83 Nov 23 2024 05:48:17
%S A019952 1,3,7,6,3,8,1,9,2,0,4,7,1,1,7,3,5,3,8,2,0,7,2,0,9,5,8,1,9,1,0,8,8,7,
%T A019952 6,7,9,5,2,5,8,9,9,3,3,6,0,0,8,1,5,8,6,6,3,3,6,5,6,7,5,7,6,5,6,1,9,0,
%U A019952 9,5,1,9,3,7,6,7,1,7,2,9,8,5,0,6,5,9,5,2,9,9,3,1,1,0,0,7,0,1,9
%N A019952 Decimal expansion of tangent of 54 degrees.
%C A019952 Also the decimal expansion of cotangent of 36 degrees. - _Mohammad K. Azarian_, Jun 30 2013
%C A019952 A quartic number with denominator 5. - _Charles R Greathouse IV_, Aug 27 2017
%C A019952 Conjecture: Product (2/3) * (8/7) * (12/13) * (18/17) * (22/23) * (32/33) * ... * (a_n/b_n) = sqrt(25 + 10*sqrt(5))/5 = tan(3*Pi/10) = A019952, where a_n even, a_n + b_n = a(n), |a_n - b_n| = 1, n >= 0. - _Dimitris Valianatos_, Feb 14 2020
%C A019952 Also the limiting value of the distance between the lines F(n)*x + F(n+1)*y = 0 and F(n)*x + F(n+1)*y = F(n+2) (where F(n)=A000045(n) are the Fibonacci numbers and n>0). - _Burak Muslu_, Apr 03 2021
%C A019952 Decimal expansion of the radius of an inscribed sphere in a rhombic triacontahedron with unit edge length. - _Wesley Ivan Hurt_, May 11 2021
%H A019952 Ivan Panchenko, <a href="/A019952/b019952.txt">Table of n, a(n) for n = 1..1000</a>
%H A019952 Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>.
%H A019952 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rhombic_triacontahedron">Rhombic triacontahedron</a>.
%H A019952 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A019952 Equals A019863/A019845 = 1/A019934. - _R. J. Mathar_, Jul 26 2010
%F A019952 The largest positive solution of cos(4*arctan(1/x)) = cos(6*arctan(1/x)). - _Thomas Olson_, Oct 03 2014
%F A019952 Equals sqrt(25 + 10*sqrt(5))/5. - _G. C. Greubel_, Nov 22 2018
%F A019952 Equals sqrt(2 + sqrt(5))/5^(1/4). - _Burak Muslu_, Apr 03 2021
%F A019952 From _Wesley Ivan Hurt_, May 11 2021: (Start)
%F A019952 Equals phi^2/sqrt(1+phi^2) where phi is the golden ratio.
%F A019952 Equals sqrt(1+2/sqrt(5)). (End)
%F A019952 Equals Product_{k>=1} (1 - (-1)^k/A090772(k)). - _Amiram Eldar_, Nov 23 2024
%F A019952 Equals 2*A375067. - _Hugo Pfoertner_, Nov 23 2024
%e A019952 1.376381920471173538207209581910887679525899336...
%p A019952 Digits:=100: evalf(tan(3*Pi/10)); # _Wesley Ivan Hurt_, Oct 07 2014
%t A019952 RealDigits[Tan[3*Pi/10], 10, 100][[1]] (* _Wesley Ivan Hurt_, Oct 07 2014 *)
%t A019952 RealDigits[Tan[54 Degree],10,120][[1]] (* _Harvey P. Dale_, Jul 16 2016 *)
%o A019952 (PARI) tan(3*Pi/10) \\ _Charles R Greathouse IV_, Aug 27 2017
%o A019952 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Tan(3*Pi(R)/10); // _G. C. Greubel_, Nov 22 2018
%o A019952 (Sage) numerical_approx(tan(3*pi/10), digits=100) # _G. C. Greubel_, Nov 22 2018
%o A019952 (Python)
%o A019952 from sympy import sqrt
%o A019952 [print(i, end=', ') for i in str(sqrt(1+2/sqrt(5)).n(110)) if i!='.'] # _Karl V. Keller, Jr._, Jun 19 2020
%Y A019952 Cf. A019845, A019863, A019934, A090772, A375067.
%Y A019952 Cf. A344171 (rhombic triacontahedron surface area).
%Y A019952 Cf. A344172 (rhombic triacontahedron volume).
%Y A019952 Cf. A344212 (rhombic triacontahedron midradius).
%K A019952 nonn,cons
%O A019952 1,2
%A A019952 _N. J. A. Sloane_