|
%I #20 Jul 09 2023 02:53:28
%S 1,2,1,8,2,8,2,9,0,5,0,1,7,2,7,7,6,2,1,7,6,0,4,6,1,7,6,8,9,1,5,7,9,7,
%T 9,4,1,7,3,9,1,3,1,9,4,9,4,6,8,1,5,6,5,0,5,0,4,9,6,6,0,2,6,2,9,4,8,1,
%U 7,8,2,1,6,3,0,0,7,6,0,7,6,3,7,6,1,9,6,9,1,6,8,1,5,5,7,7,2,1,3,0,7,0,2,8,6
%N Decimal expansion of arctan(e).
%C The slope of the unique straight line passing through the origin which kisses the exponential function y=exp(x), i.e., the angle (in radians) the tangent line subtends with the X axis. The kissing point coordinates are (1,e).
%H Stanislav Sykora, <a href="/A257777/b257777.txt">Table of n, a(n) for n = 1..2000</a>
%H Robert Frontczak, <a href="https://nntdm.net/volume-23-2017/number-1/39-53/">Further results on arctangent sums with applications to generalized Fibonacci numbers</a>, Notes on Number Theory and Discrete Mathematics, Vol. 23, No. 1 (2017), pp. 39-53.
%F Equals (Sum_{k>=0} arctan(sinh(1)/cosh(k))) - Pi/4 (Frontczak, 2017, eq. (3.22)). - _Amiram Eldar_, Jul 09 2023
%e 1.21828290501727762176046176891579794173913194946815650504966...
%e In degrees:
%e 69.8024687104273501888256538674056059123933374409546355361989953970...
%t RealDigits[ArcTan[E],10,105][[1]] (* _Vaclav Kotesovec_, Jun 02 2015 *)
%o (PARI) atan(exp(1))
%Y Cf. A001113, A248618, A257775, A257776, A257896, A258428.
%K nonn,cons,easy
%O 1,2
%A _Stanislav Sykora_, May 12 2015
|
