A198101 Decimal expansion of greatest x having x^2-4x=-2*cos(x).

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

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: 0.50130475545480646339369035756819...
greatest x: 4.222749528794927324484249676610...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 1; b = -4; c = -2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, 0, 5}]
r1 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]
RealDigits[r1] (* A198100 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 4.2, 4.3}, WorkingPrecision -> 110]
RealDigits[r2] (* A198101 *)