A200305 Decimal expansion of least x satisfying 4*x^2 - 4*cos(x) = sin(x), negated.

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

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

Index entries for transcendental numbers.

Example

least x: -0.749483556259155223568363487735793...
greatest x: 0.90305961390486425091022746455261...

Mathematica

a = 4; 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, -.75, -.74}, WorkingPrecision -> 110]
RealDigits[r]   (* A200305 *)
r = x /. FindRoot[f[x] == g[x], {x, .90, .91}, WorkingPrecision -> 110]
RealDigits[r]    (* A200306 *)

Prog

(PARI) a=4; b=-4; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 08 2018

Crossrefs

Cf. A199949.

Sequence in context: A178768 A008568 A019795 * A199448 A110644 A117028

Adjacent sequences: A200302 A200303 A200304 * A200306 A200307 A200308

Keyword

nonn,cons,changed

Author

Clark Kimberling, Nov 16 2011

Status

approved