A198214 Decimal expansion of least x having 3*x^2+x=cos(x).

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

Offset: 0

Author

Clark Kimberling, Oct 22 2011

Keywords

• nonn
• cons

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -0.6986567055323602628379046584016603229...
greatest x: 0.41073056810531967884261632168842932...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 3; b = 1; c = 1;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -.7, -0.6}, WorkingPrecision -> 110]
RealDigits[r1]  (* A198214 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 4.1, 4.2}, WorkingPrecision -> 110]
RealDigits[r2] (* A198215 *)