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A200238 Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = sin(x). 3
9, 3, 0, 0, 5, 7, 1, 1, 0, 0, 9, 2, 4, 8, 9, 2, 4, 6, 7, 8, 8, 2, 4, 6, 8, 1, 4, 4, 0, 5, 6, 4, 2, 9, 8, 7, 6, 1, 2, 8, 2, 5, 6, 1, 0, 1, 9, 3, 3, 3, 0, 7, 7, 4, 3, 6, 2, 1, 4, 0, 0, 8, 2, 0, 5, 2, 4, 8, 3, 3, 0, 7, 8, 7, 5, 2, 4, 1, 7, 9, 3, 2, 7, 7, 1, 6, 9, 0, 3, 3, 2, 7, 7, 5, 3, 4, 1, 1, 2 (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: -0.725773931375098148951813264652313...

greatest x: 0.9300571100924892467882468144056...

MATHEMATICA

a = 3; 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, -.73, -.72}, WorkingPrecision -> 110]

RealDigits[r]   (* A200237 *)

r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]

RealDigits[r]   (* A200238 *)

PROG

(PARI) a=3; b=-3; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 05 2018

CROSSREFS

Cf. A199949.

Sequence in context: A096042 A038292 A294685 * A254666 A094127 A198924

Adjacent sequences:  A200235 A200236 A200237 * A200239 A200240 A200241

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 15 2011

STATUS

approved

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Last modified November 21 12:11 EST 2019. Contains 329370 sequences. (Running on oeis4.)