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A200129 Decimal expansion of greatest x satisfying 2*x^2-4*cos(x)=sin(x). 3
1, 1, 3, 7, 4, 0, 1, 1, 9, 9, 5, 2, 6, 8, 6, 8, 5, 2, 6, 5, 0, 2, 7, 8, 8, 0, 3, 0, 8, 4, 2, 5, 4, 4, 8, 8, 0, 5, 3, 0, 2, 1, 1, 9, 6, 5, 1, 5, 2, 5, 1, 3, 6, 5, 2, 7, 2, 9, 1, 7, 5, 8, 7, 9, 5, 2, 0, 9, 9, 5, 9, 6, 1, 9, 0, 2, 0, 3, 1, 5, 1, 9, 0, 1, 7, 9, 8, 3, 6, 9, 7, 0, 1, 2, 9, 6, 8, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A199949 for a guide to related sequences.  The Mathematica program includes a graph.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

least x: -0.91125136577248241254947318280293...

greatest x: 1.13740119952686852650278803084...

MATHEMATICA

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

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, -.92, -.91}, WorkingPrecision -> 110]

RealDigits[r]  (* A200128 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.13, 1.14}, WorkingPrecision -> 110]

RealDigits[r]  (* A200129 *)

CROSSREFS

Cf. A199949.

Sequence in context: A213244 A050393 A110778 * A181912 A108297 A135928

Adjacent sequences:  A200126 A200127 A200128 * A200130 A200131 A200132

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 14 2011

STATUS

approved

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Last modified April 20 05:05 EDT 2014. Contains 240779 sequences.