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A200023 Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 3*sin(x). 3
1, 6, 6, 9, 6, 9, 2, 1, 6, 9, 6, 4, 9, 7, 6, 3, 4, 5, 8, 2, 5, 2, 8, 3, 8, 3, 0, 5, 9, 8, 4, 9, 1, 7, 3, 3, 5, 9, 3, 7, 7, 5, 8, 9, 9, 6, 5, 9, 1, 6, 9, 9, 1, 6, 8, 2, 8, 2, 4, 0, 8, 4, 9, 6, 1, 1, 2, 9, 1, 0, 5, 6, 2, 3, 4, 4, 1, 3, 3, 4, 1, 9, 3, 2, 5, 7, 8, 3, 8, 7, 2, 9, 5, 5, 6, 9, 3, 4, 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:  -0.514514830476458686565638945675371815952...

greatest x: 1.66969216964976345825283830598491733593...

MATHEMATICA

a = 1; b = -2; c = 3;

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, -.52, -.51}, WorkingPrecision -> 110]

RealDigits[r]  (* A200022 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.66, 1.67}, WorkingPrecision -> 110]

RealDigits[r]  (* A200023 *)

PROG

(PARI) a=1; b=-2; c=3; 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: A250721 A065480 A198116 * A198115 A291545 A205372

Adjacent sequences:  A200020 A200021 A200022 * A200024 A200025 A200026

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 13 2011

STATUS

approved

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Last modified August 24 16:21 EDT 2019. Contains 326295 sequences. (Running on oeis4.)