cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A257777 Decimal expansion of arctan(e).

Original entry on oeis.org

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, 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, 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
Offset: 1

Views

Author

Stanislav Sykora, May 12 2015

Keywords

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).

Examples

			1.21828290501727762176046176891579794173913194946815650504966...
In degrees:
69.8024687104273501888256538674056059123933374409546355361989953970...
		

Crossrefs

Programs

  • Mathematica
    RealDigits[ArcTan[E],10,105][[1]] (* Vaclav Kotesovec, Jun 02 2015 *)
  • PARI
    atan(exp(1))

Formula

Equals (Sum_{k>=0} arctan(sinh(1)/cosh(k))) - Pi/4 (Frontczak, 2017, eq. (3.22)). - Amiram Eldar, Jul 09 2023