A196822 - OEIS

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A196822

Decimal expansion of the number x satisfying 2*x = ((1+x^2)^2)*sin(x) and 0 < x < 2*Pi.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..105.

EXAMPLE

x=0.686928072507114151477426614944457695958221498999...

MATHEMATICA

Plot[{1/(1 + x^2), -.097 + Cos[x]}, {x, 0, 1}]

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

RealDigits[t] (* A196822 *)

c = N[-Cos[t] + 1/(1 + t^2), 100]