A199611 Decimal expansion of least x satisfying x+4*cos(x)=0.

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

Offset: 1

Author

Clark Kimberling, Nov 08 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: -1.25235323400258876318632812197538043590128...
greatest:  3.59530486716154799187760693508341871491...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 4; c = 0;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199611, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199612, greatest of 4 roots *)