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A199964 Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 3*sin(x). 3
2, 1, 7, 8, 8, 4, 3, 3, 0, 3, 0, 3, 8, 4, 3, 8, 4, 7, 8, 7, 4, 7, 3, 5, 1, 5, 4, 6, 6, 3, 1, 1, 2, 0, 7, 8, 8, 0, 9, 8, 3, 8, 5, 5, 8, 5, 8, 9, 3, 8, 0, 7, 1, 9, 4, 3, 7, 4, 9, 0, 8, 7, 6, 0, 0, 4, 7, 5, 6, 4, 2, 6, 7, 4, 4, 8, 5, 4, 0, 4, 7, 5, 3, 2, 0, 2, 9, 5, 4, 4, 4, 8, 4, 5, 2, 5, 9, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 = 1..10000

EXAMPLE

least x:  1.2397511548307033226630942987091820...

greatest x: 2.17884330303843847874735154663112...

MATHEMATICA

a = 1; b = 4; c = 3;

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

Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, 1.23, 1.24}, WorkingPrecision -> 110]

RealDigits[r]   (* A199963 *)

r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]

RealDigits[r]  (* A199964 *)

PROG

(PARI) a=1; b=4; c=3; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

Cf. A199949.

Sequence in context: A157240 A144749 A021463 * A217107 A320432 A141513

Adjacent sequences:  A199961 A199962 A199963 * A199965 A199966 A199967

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 12 2011

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)