A200026 Decimal expansion of least x satisfying x^2 - 3*cos(x) = sin(x) (negated).

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

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:  -0.9559087984816134135373014395844...
greatest x: 1.31448560919776196551921986761091...

Mathematica

a = 1; 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, -.96, -.95}, WorkingPrecision -> 110]
RealDigits[r]  (* A200026 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.31, 1.34}, WorkingPrecision -> 110]
RealDigits[r]  (* A200027 *)

Prog

(PARI) a=1; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

Crossrefs

Cf. A199949.

Sequence in context: A197838 A155534 A154683 * A262276 A244844 A255896

Adjacent sequences: A200023 A200024 A200025 * A200027 A200028 A200029

Keyword

nonn,cons

Author

Clark Kimberling, Nov 13 2011

Status

approved