A199604 Decimal expansion of greatest x satisfying x+3*cos(x) = 0.

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

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: -1.1701209500026260537060430118589710...
greatest:  2.9381003939708118076581364784259...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 3; c = 0;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199603 least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 2.93, 2.94}, WorkingPrecision -> 110]
RealDigits[r]  (* A199604 greatest of 4 roots *)

Extensions

a(86) onwards corrected by Georg Fischer, Aug 03 2021