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A200096 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 3*sin(x). 3
1, 6, 5, 4, 6, 9, 9, 7, 8, 2, 2, 9, 3, 9, 0, 1, 0, 7, 1, 1, 3, 1, 6, 8, 6, 6, 8, 1, 8, 3, 0, 8, 0, 0, 6, 3, 5, 4, 6, 5, 9, 6, 8, 5, 5, 6, 7, 0, 3, 5, 0, 6, 3, 0, 7, 5, 3, 8, 7, 7, 2, 4, 0, 1, 0, 7, 0, 3, 8, 7, 2, 6, 4, 8, 7, 7, 0, 4, 0, 0, 3, 7, 8, 7, 1, 8, 7, 6, 8, 5, 2, 5, 7, 6, 2, 3, 7, 1, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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:  -0.677119411697943130184179520098917021...

greatest x: 1.6546997822939010711316866818308006354...

MATHEMATICA

a = 1; b = -3; 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, -.88, -.67}, WorkingPrecision -> 110]

RealDigits[r]  (* A200095 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]

RealDigits[r]  (* A200096 *)

PROG

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

CROSSREFS

Cf. A199949.

Sequence in context: A302712 A125089 A171537 * A220086 A094773 A205651

Adjacent sequences:  A200093 A200094 A200095 * A200097 A200098 A200099

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 13 2011

STATUS

approved

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Last modified April 22 06:35 EDT 2019. Contains 322329 sequences. (Running on oeis4.)