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

Offset: 0

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			x=0.686928072507114151477426614944457695958221498999...
		

Crossrefs

Cf. A196823.

Programs

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]
RealDigits[c]     (* A196823 *)
slope = N[-Sin[t], 100]
RealDigits[slope] (* A196824 *)

Extensions

Definition and a(84) onwards corrected by Georg Fischer, Aug 10 2021