A200281 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 3*sin(x), negated.

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

Offset

0,1

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

least x: -0.6615723781879899920628993073289...
greatest x: 1.19240455007681565929009549661...

Mathematica

a = 3; b = -4; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
RealDigits[r]    (* A200281 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]   (* A200282 *)

Prog

(PARI) a=3; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018

Crossrefs

Cf. A199949.

Sequence in context: A248059 A111719 A228918 * A199864 A153605 A247447

Adjacent sequences: A200278 A200279 A200280 * A200282 A200283 A200284

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved