A257777 - OEIS

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A257777

Decimal expansion of arctan(e).

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

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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