A200018 Decimal expansion of least x satisfying x^2 - 2*cos(x) = sin(x) (negated).

8, 0, 9, 6, 2, 9, 9, 9, 9, 1, 2, 9, 5, 5, 2, 4, 1, 3, 1, 8, 6, 1, 0, 9, 6, 9, 8, 4, 8, 4, 0, 2, 7, 1, 3, 2, 1, 9, 6, 6, 9, 1, 7, 6, 0, 3, 5, 6, 5, 4, 5, 3, 7, 8, 5, 3, 8, 9, 4, 7, 8, 4, 6, 3, 2, 9, 8, 3, 6, 9, 0, 8, 2, 3, 2, 1, 6, 6, 6, 8, 3, 9, 6, 9, 0, 1, 7, 5, 9, 9, 6, 0, 8, 6, 5, 1, 2, 5, 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:  -0.8096299991295524131861096984840271321...
greatest x: 1.254187962477919553363912326321801374...

Mathematica

a = 1; b = -2; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]
RealDigits[r]  (* A200018 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]  (* A200019 *)

Prog

(PARI) a=1; b=-2; 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: A154803 A166529 A245293 * A019937 A176460 A320378

Adjacent sequences: A200015 A200016 A200017 * A200019 A200020 A200021

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved