A200278 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = sin(x).

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

Offset

1,5

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 = 1..10000

Example

least x: -0.81771521879230454511191454208365777...
greatest x: 1.000303639283590185187225035744180...

Mathematica

a = 3; b = -4; c = 1;
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, -.82, -.81}, WorkingPrecision -> 110]
RealDigits[r]   (* A200277  *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A200278 *)

Prog

(PARI) a=3; b=-4; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 05 2018

Crossrefs

Cf. A199949.

Sequence in context: A258108 A282610 A011076 * A247734 A010599 A226568

Adjacent sequences: A200275 A200276 A200277 * A200279 A200280 A200281

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved