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A196913 Decimal expansion of the number x satisfying 0<x<2*pi and 2x=(1+x^2)*tan(x). 3
7, 6, 8, 2, 1, 7, 1, 5, 5, 3, 1, 5, 3, 7, 8, 2, 5, 0, 4, 3, 1, 2, 1, 2, 2, 8, 6, 6, 9, 7, 9, 2, 5, 4, 0, 9, 5, 4, 6, 6, 9, 1, 5, 6, 5, 8, 5, 7, 1, 6, 3, 2, 1, 6, 7, 1, 9, 4, 9, 1, 6, 8, 4, 5, 8, 8, 1, 3, 4, 3, 5, 2, 8, 9, 3, 3, 1, 2, 0, 8, 9, 2, 5, 6, 2, 2, 8, 9, 9, 7, 6, 8, 7, 3, 7, 7, 1, 4, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..99.

EXAMPLE

x=0.7682171553153782504312122866979254095466915658...

MATHEMATICA

Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]

t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]

RealDigits[t]    (* A196913 *)

c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]

RealDigits[c]    (* A196914 *)

slope = N[-c*Sin[t], 100]

RealDigits[slope](* A196915 *)

CROSSREFS

Cf. A196816, A196914.

Sequence in context: A202345 A010512 A195370 * A091343 A196397 A238301

Adjacent sequences:  A196910 A196911 A196912 * A196914 A196915 A196916

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 07 2011

STATUS

approved

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Last modified December 19 16:00 EST 2014. Contains 252236 sequences.