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A248618 Decimal expansion of the solution when inverse Gudermannian(x) equals 1. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

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

Wikipedia, Gudermannian function

FORMULA

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

EXAMPLE

0.86576948323965862428960184619184444137967919924876009961184822974244822945841...

The wedge angle in degrees:

49.6049374208547003776513077348112118247866748819092710723979907940346891648208... - Stanislav Sykora, May 31 2015

MAPLE

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

MATHEMATICA

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

PROG

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

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

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

CROSSREFS

Cf. A248617, A257777, A258428.

Sequence in context: A021540 A100199 A161883 * A197329 A046266 A165104

Adjacent sequences:  A248615 A248616 A248617 * A248619 A248620 A248621

KEYWORD

nonn,cons

AUTHOR

Robert G. Wilson v, Oct 09 2014

STATUS

approved

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Last modified January 22 13:36 EST 2020. Contains 331149 sequences. (Running on oeis4.)