A199731 Decimal expansion of least x satisfying x^2-4*x*cos(x)=4*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 09 2011

Keywords

• nonn
• cons

Comments

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least: -3.80284270062359171640437975188554983520...
greatest:  1.71776170155914673794654693768308401...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = -4; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.9, -3.8}, WorkingPrecision -> 110]
RealDigits[r]   (* A199731 least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]
RealDigits[r]   (* A199732 greatest of 4 roots *)