A200226 Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = 3*sin(x).

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

Offset

1,4

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: -0.25837586008348694859843826122973...
greatest x: 1.012265562969209417334554419938...

Mathematica

a = 3; b = -1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.26, -.25}, WorkingPrecision -> 110]
RealDigits[r]    (* A200225 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]    (* A200226 *)

Prog

(PARI) a=3; b=-1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 30 2018

Crossrefs

Cf. A199949.

Sequence in context: A144160 A368228 A275142 * A300628 A379822 A115255

Adjacent sequences: A200223 A200224 A200225 * A200227 A200228 A200229

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved