A248617 -id:A248617 - cp's OEIS frontend

A248618 Decimal expansion of the solution when inverse Gudermannian(x) equals 1.

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

Offset: 0

Robert G. Wilson v, Oct 09 2014

Inverse of A248617.

This is the angle of the unique wedge having its apex at the origin and kissing the exponential curve y=exp(x) on one side, and its inverse logarithmic function y=log(x) on the other side. - Stanislav Sykora, May 31 2015

			0.86576948323965862428960184619184444137967919924876009961184822974244822945841...
The wedge angle in degrees:
49.6049374208547003776513077348112118247866748819092710723979907940346891648208... - _Stanislav Sykora_, May 31 2015

Stanislav Sykora, Table of n, a(n) for n = 0..2000
Wikipedia, Gudermannian function.

Cf. A248617, A257777, A258428.

evalf(arcsin((exp(2)-1)/(exp(2)+1)),100) # Vaclav Kotesovec, Oct 11 2014

RealDigits[ Gudermannian[ 1], 10, 111][[1]]

asin((exp(2)-1)/(exp(2)+1)) \\ Michel Marcus, Oct 11 2014

atan(exp(1))-atan(1/exp(1)) \\ Stanislav Sykora, May 31 2015

2*atan(exp(1))-Pi/2 \\ Charles R Greathouse IV, Jun 02 2015

Equals arcsin((exp(2)-1)/(exp(2)+1)). - Vaclav Kotesovec, Oct 11 2014
Equals atan(e)-atan(1/e) = A257777-A258428. - Stanislav Sykora, May 31 2015
From Amiram Eldar, Apr 07 2022: (Start)
Equals 2*arctan(tanh(1/2)).
Equals Integral_{x=0..1} sech(x) dx. (End)

A384932 Decimal expansion of tan(1) + sec(1).

Original entry on oeis.org

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

Offset: 1

Kritsada Moomuang, Jun 12 2025

The continued fraction expansion of this constant - 1 is A133265.

			3.408223442335827848481...

Cf. A049471, A073448, A133265, A248617.

RealDigits[Tan[1] + Sec[1], 10, 100, 0][[1]]

tan(1) + 1/cos(1) \\ Amiram Eldar, Jun 13 2025

Equals A049471 + A073448.
Equals 4 + Integral_{x=0..1} sin(x)/(sin(x) - 1) dx.
Equals exp(Integral_{x=0..1} sec(x) dx).
Equals exp(A248617). - Hugo Pfoertner, Jun 13 2025

cp's OEIS Frontend

A248618 Decimal expansion of the solution when inverse Gudermannian(x) equals 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

PARI

Formula

A384932 Decimal expansion of tan(1) + sec(1).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Formula