OFFSET
1,2
COMMENTS
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).
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..2000
Robert Frontczak, Further results on arctangent sums with applications to generalized Fibonacci numbers, Notes on Number Theory and Discrete Mathematics, Vol. 23, No. 1 (2017), pp. 39-53.
FORMULA
Equals (Sum_{k>=0} arctan(sinh(1)/cosh(k))) - Pi/4 (Frontczak, 2017, eq. (3.22)). - Amiram Eldar, Jul 09 2023
EXAMPLE
1.21828290501727762176046176891579794173913194946815650504966...
In degrees:
69.8024687104273501888256538674056059123933374409546355361989953970...
MATHEMATICA
RealDigits[ArcTan[E], 10, 105][[1]] (* Vaclav Kotesovec, Jun 02 2015 *)
PROG
(PARI) atan(exp(1))
CROSSREFS
KEYWORD
AUTHOR
Stanislav Sykora, May 12 2015
STATUS
approved