

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
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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



