A258428 Decimal expansion of arctan(1/e).

3, 5, 2, 5, 1, 3, 4, 2, 1, 7, 7, 7, 6, 1, 8, 9, 9, 7, 4, 7, 0, 8, 5, 9, 9, 2, 2, 7, 2, 3, 9, 5, 3, 5, 0, 0, 3, 5, 9, 4, 5, 2, 7, 5, 0, 2, 1, 9, 3, 9, 6, 4, 0, 5, 4, 3, 7, 8, 1, 2, 0, 3, 3, 2, 0, 5, 7, 2, 9, 9, 8, 6, 8, 4, 2, 3, 4, 3, 7, 3, 5, 5, 5, 2, 0, 4, 8, 2, 4, 4, 5, 1, 5, 2, 8, 6, 4, 0, 3, 2, 8, 8, 2, 1, 0

Offset: 0

Author

Stanislav Sykora, May 31 2015

Keywords

• nonn
• cons

Comments

The slope of the unique straight line passing through the origin which kisses the logarithmic function y=log(x), i.e., the angle (in radians) the tangent line subtends with the X axis. The kissing point coordinates are (e,1).

Examples

			0.35251342177761899747085992272395350035945275021939640543781203320...
In degrees:
20.1975312895726498111743461325943940876066625590453644638010046029...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A001113, A257777, A248618.

Programs

Mathematica

RealDigits[ArcTan[Exp[-1]],10,105][[1]] (* Vaclav Kotesovec, Jun 02 2015 *)

PARI

atan(1/exp(1))

Formula

Equals Integral_{x=1..oo} 1/(2*cosh(x)) dx. - Amiram Eldar, Aug 10 2020