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A200004 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 4*sin(x). 3
2, 8, 4, 1, 5, 5, 4, 2, 5, 1, 7, 7, 1, 4, 8, 1, 4, 9, 1, 6, 8, 0, 5, 3, 6, 2, 8, 8, 7, 3, 5, 4, 4, 3, 3, 1, 0, 5, 0, 2, 6, 1, 5, 3, 6, 0, 2, 5, 8, 1, 3, 5, 3, 6, 8, 0, 9, 3, 6, 7, 6, 7, 1, 4, 5, 7, 3, 3, 4, 3, 5, 2, 2, 1, 4, 0, 1, 8, 7, 8, 6, 5, 4, 8, 3, 5, 5, 8, 2, 8, 9, 0, 5, 2, 9, 2, 9, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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 = 0..10000

EXAMPLE

least x:  0.2841554251771481491680536288735443310...

greatest x: 1.36083225539066890467183928569132636...

MATHEMATICA

a = 2; b = 1; 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, .28, .29}, WorkingPrecision -> 110]

RealDigits[r]   (* A200004 *)

r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]

RealDigits[r]   (* A200005 *)

PROG

(PARI) a=2; b=1; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

Cf. A199949.

Sequence in context: A030345 A264818 A264709 * A253634 A152626 A093823

Adjacent sequences:  A200001 A200002 A200003 * A200005 A200006 A200007

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 12 2011

STATUS

approved

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Last modified August 14 07:59 EDT 2020. Contains 336477 sequences. (Running on oeis4.)