|
%I #45 Apr 23 2024 05:16:22
%S 5,7,2,8,9,9,6,1,6,3,0,7,5,9,4,2,4,6,8,7,2,7,8,1,4,7,5,3,7,1,1,2,5,7,
%T 7,9,8,0,2,1,7,5,2,2,2,3,5,1,4,3,9,2,6,4,7,2,5,8,1,1,0,3,6,0,6,5,2,9,
%U 2,2,8,9,3,6,4,7,9,1,9,3,0,6,7,2,4,1,6,2,8,2,2,0,6,8,3,8,8,0,6
%N Decimal expansion of tangent of 89 degrees.
%C Also cotangent of 1 degree. - _Mohammad K. Azarian_, Jan 21 2006
%C An algebraic integer of degree 24. - _Charles R Greathouse IV_, Aug 27 2017
%C The least k > 0 such that floor(cot(1°)*10^k) is prime is k = 39. - _M. F. Hasler_, May 19 2023
%H Ivan Panchenko, <a href="/A019987/b019987.txt">Table of n, a(n) for n = 2..1000</a>.
%H Art of Problem Solving, <a href="https://artofproblemsolving.com/wiki/index.php/1996_USAMO_Problems/Problem_1">USAMO 1996, Problem 1</a>.
%H Mohammad K. Azarian, <a href="http://www.jstor.org/stable/30044897">Forty-Five Nested Equilateral Triangles and cosecant of 1 degree, Problem 813</a>, College Mathematics Journal, Vol. 36, No. 5, November 2005, p. 413-414; <a href="http://www.jstor.org/stable/27646393">Solution</a>, College Mathematics Journal, Vol. 37, No. 5, November 2006, pp. 394-395.
%H User ssaamil, <a href="https://www.reddit.com/r/math/comments/13fcvhz">I found a cool number I'd like to share, 57289961630759424687278147537112577980217</a>. In reddit.com/r/math, May 12 2023
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%H <a href="/index/Al#algebraic_24">Index entries for algebraic numbers, degree 24</a>
%F Equals (Sum_{k=1..90} 2*k*sin(2*k)) / 90, with k in degrees (link USAMO 1996). - _Bernard Schott_, Apr 30 2022
%e 57.28996...
%p evalf(cot(Pi/180),100); # _Bernard Schott_, Apr 30 2022
%t First[RealDigits[Cot[Pi/180], 10, 100]] (* _Paolo Xausa_, Apr 23 2024 *)
%o (PARI) tan(89*Pi/180) \\ _Charles R Greathouse IV_, Aug 27 2017
%Y Cf. A073449, A019899-A019986 (same for 1, ..., 88 degrees).
%K nonn,cons,changed
%O 2,1
%A _N. J. A. Sloane_.
%E Edited by _N. J. A. Sloane_, Aug 19 2008 at the suggestion of _R. J. Mathar_
|
