A197820 Decimal expansion of greatest x having x^2-2x=-cos(x).

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

Offset: 1

Author

Clark Kimberling, Oct 20 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: 0.589303208159012874725223919073869185889...
greatest x: 2.287086177656584485337033312314491737...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 1; b = -2; c = -1;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 3}]
r1 = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r1] (* A197815 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
RealDigits[r2] (* A197820  *)