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A200294 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = sin(x). 3
7, 3, 3, 9, 7, 2, 6, 2, 7, 9, 4, 0, 2, 8, 9, 6, 1, 4, 3, 3, 4, 5, 0, 5, 0, 5, 6, 0, 0, 3, 9, 2, 9, 9, 2, 2, 0, 8, 5, 4, 5, 1, 3, 5, 6, 9, 6, 3, 5, 3, 9, 8, 1, 5, 0, 7, 6, 2, 5, 5, 4, 7, 2, 6, 5, 7, 2, 8, 2, 7, 5, 2, 5, 7, 8, 5, 8, 9, 3, 8, 3, 1, 7, 1, 7, 4, 0, 3, 8, 2, 6, 2, 1, 8, 4, 2, 6, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
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: -0.5455973884814757395042148847857...

greatest x: 0.73397262794028961433450505600...

MATHEMATICA

a = 4; b = -2; c = 1;

f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -.55, -.54}, WorkingPrecision -> 110]

RealDigits[r]   (* A200293 *)

r = x /. FindRoot[f[x] == g[x], {x, .73, .74}, WorkingPrecision -> 110]

RealDigits[r]   (* A200294 *)

PROG

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

CROSSREFS

Cf. A199949.

Sequence in context: A011299 A225453 A153858 * A169813 A097517 A127559

Adjacent sequences:  A200291 A200292 A200293 * A200295 A200296 A200297

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 15 2011

STATUS

approved

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Last modified October 20 15:29 EDT 2019. Contains 328267 sequences. (Running on oeis4.)