A200238 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = sin(x).

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

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: -0.725773931375098148951813264652313...
greatest x: 0.9300571100924892467882468144056...

Mathematica

a = 3; b = -3; 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, -.73, -.72}, WorkingPrecision -> 110]
RealDigits[r]   (* A200237 *)
r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
RealDigits[r]   (* A200238 *)

Prog

(PARI) a=3; b=-3; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 05 2018

Crossrefs

Cf. A199949.

Sequence in context: A096042 A038292 A294685 * A368982 A254666 A094127

Adjacent sequences: A200235 A200236 A200237 * A200239 A200240 A200241

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved