A198114 Decimal expansion of least x having 2*x^2+x=2*cos(x).

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

Offset: 1

Author

Clark Kimberling, Oct 21 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -1.01705490067506096933116558361774...
greatest x: 0.66996816904693319175093928956216628...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 2; b = 1; c = 2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.02, -1.01}, WorkingPrecision -> 110]
RealDigits[r1](* A198114 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .66, .67}, WorkingPrecision -> 110]
RealDigits[r2](* A198115 *)