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A200025 Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 4*sin(x). 3
1, 8, 3, 0, 7, 3, 3, 4, 5, 3, 2, 9, 0, 8, 6, 3, 5, 9, 9, 2, 1, 0, 2, 3, 5, 9, 5, 4, 7, 3, 4, 1, 4, 7, 8, 8, 4, 5, 3, 6, 6, 7, 8, 1, 2, 8, 3, 2, 4, 2, 1, 4, 9, 5, 2, 2, 9, 5, 8, 1, 6, 4, 2, 6, 7, 1, 0, 0, 0, 8, 5, 1, 1, 9, 4, 6, 2, 3, 6, 2, 0, 3, 8, 0, 5, 5, 4, 6, 3, 7, 8, 8, 4, 3, 4, 1, 1, 3, 7 (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:  -0.42352729471869116185741155509692883402...

greatest x: 1.8307334532908635992102359547341478845...

MATHEMATICA

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

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, -.43, -.42}, WorkingPrecision -> 110]

RealDigits[r]  (* A200024 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.83, 1.84}, WorkingPrecision -> 110]

RealDigits[r]  (* A200025 *)

PROG

(PARI) a=1; b=-2; c=4; 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: A154538 A154166 A010521 * A200300 A268440 A137433

Adjacent sequences:  A200022 A200023 A200024 * A200026 A200027 A200028

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 13 2011

STATUS

approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)