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A200013 Decimal expansion of greatest x satisfying x^2 - cos(x) = 2*sin(x). 3
1, 4, 5, 0, 9, 3, 8, 4, 4, 9, 6, 3, 4, 9, 7, 4, 4, 3, 1, 1, 2, 8, 2, 8, 5, 5, 7, 6, 6, 9, 0, 3, 5, 7, 7, 3, 8, 9, 4, 4, 7, 4, 8, 7, 0, 1, 1, 5, 3, 4, 6, 3, 9, 8, 7, 6, 5, 4, 2, 3, 5, 8, 6, 2, 6, 2, 9, 6, 1, 9, 2, 8, 4, 3, 0, 8, 1, 3, 5, 0, 5, 9, 1, 7, 2, 0, 8, 4, 3, 0, 4, 9, 7, 0, 9, 4, 6, 6, 0 (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:  -0.3941241928589759600997053993545900...

greatest x: 1.450938449634974431128285576690357...

MATHEMATICA

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

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

Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]

RealDigits[r]   (* A200012 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

RealDigits[r]   (* A200013 *)

PROG

(PARI) a=1; b=-1; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

Cf. A199949.

Sequence in context: A240160 A249860 A320162 * A178219 A322232 A232397

Adjacent sequences:  A200010 A200011 A200012 * A200014 A200015 A200016

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 12 2011

STATUS

approved

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Last modified October 16 23:46 EDT 2019. Contains 328103 sequences. (Running on oeis4.)