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A200027 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = sin(x). 3
1, 3, 1, 4, 4, 8, 5, 6, 0, 9, 1, 9, 7, 7, 6, 1, 9, 6, 5, 5, 1, 9, 2, 1, 9, 8, 6, 7, 6, 1, 0, 9, 1, 0, 6, 0, 0, 1, 2, 8, 8, 8, 9, 4, 4, 1, 4, 1, 6, 8, 4, 7, 5, 3, 8, 0, 0, 2, 1, 2, 0, 7, 0, 0, 4, 7, 7, 1, 9, 8, 2, 3, 4, 9, 0, 0, 2, 9, 7, 4, 5, 7, 6, 7, 9, 0, 4, 2, 7, 1, 0, 0, 5, 0, 1, 4, 0, 6, 8 (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:  -0.9559087984816134135373014395844...

greatest x: 1.31448560919776196551921986761091...

MATHEMATICA

a = 1; 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, -.96, -.95}, WorkingPrecision -> 110]

RealDigits[r]  (* A200026 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.31, 1.34}, WorkingPrecision -> 110]

RealDigits[r]  (* A200027 *)

PROG

(PARI) a=1; b=-3; c=1; 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: A021322 A277129 A036412 * A298890 A016473 A029637

Adjacent sequences:  A200024 A200025 A200026 * A200028 A200029 A200030

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 13 2011

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)