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%I #85 Jan 12 2024 08:35:34
%S 3,7,3,2,0,5,0,8,0,7,5,6,8,8,7,7,2,9,3,5,2,7,4,4,6,3,4,1,5,0,5,8,7,2,
%T 3,6,6,9,4,2,8,0,5,2,5,3,8,1,0,3,8,0,6,2,8,0,5,5,8,0,6,9,7,9,4,5,1,9,
%U 3,3,0,1,6,9,0,8,8,0,0,0,3,7,0,8,1,1,4,6,1,8,6,7,5,7,2,4,8,5,7
%N Decimal expansion of tangent of 75 degrees.
%C An equivalent definition of this sequence: decimal expansion of x > 1 satisfying x^2 - 4*x + 1 = 0. - _Arkadiusz Wesolowski_, Nov 28 2011
%C An algebraic integer of degree 2 with minimal polynomial x^2 - 4*x + 1. - _Charles R Greathouse IV_, Oct 17 2016
%C Length of the second longest diagonal in a regular 12-gon with unit side. - _Mohammed Yaseen_, Dec 13 2020
%H G. C. Greubel, <a href="/A019973/b019973.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Ivan Panchenko)
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Exact_trigonometric_constants">Exact trigonometric constants</a>
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F Equals 2 + sqrt(3) = 2+A002194 = cotangent of 15 degrees. - _Rick L. Shepherd_, Jul 04 2004
%F Equals exp(arccosh(2)). - _Amiram Eldar_, Aug 07 2023
%F c^n = A001835(n) + (1 + sqrt(3)) * A001353(n) = A001075(n) + sqrt(3) * A001353(n); where c = 2 + sqrt(3). - _Gary W. Adamson_, Oct 14 2023
%F Equals lim_{n->infinity} S(n, 4)/ S(n-1, 4), with the S-Chebyshev polynomial (see A049310) S(n, 4) = A001353(n+1). See the A001353 formula from Oct 06 2002 by _Gary V. Richardson_. - _Wolfdieter Lang_, Nov 15 2023
%F Equals A019884 / A019824. - _R. J. Mathar_, Jan 12 2024
%e 3.732050807568877293527446341505872366942805253810380628...
%t RealDigits[Tan[75 Degree],10,120][[1]] (* _Harvey P. Dale_, Nov 08 2011 *)
%t RealDigits[2+Sqrt[3], 10, 100][[1]] (* _G. C. Greubel_, Nov 20 2018 *)
%o (PARI) sqrt(3)+2 \\ _Charles R Greathouse IV_, Oct 17 2016
%o (Magma) SetDefaultRealField(RealField(100)); 2 + Sqrt(3); // _G. C. Greubel_, Nov 20 2018
%o (Sage) numerical_approx(2+sqrt(3), digits=100) # _G. C. Greubel_, Nov 20 2018
%Y Cf. A002194 (sqrt(3)).
%Y Cf. A001075, A001353, A001835, A049310.
%K nonn,cons,easy
%O 1,1
%A _N. J. A. Sloane_
%E Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008
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