

A199608


Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=2*sin(x).


1



3, 0, 4, 8, 1, 3, 8, 5, 9, 5, 3, 6, 5, 1, 1, 6, 6, 8, 9, 1, 4, 4, 6, 0, 5, 0, 5, 9, 3, 7, 3, 9, 0, 5, 2, 2, 0, 8, 5, 4, 6, 4, 6, 8, 6, 6, 9, 9, 5, 5, 4, 2, 6, 9, 2, 1, 5, 9, 2, 4, 3, 6, 0, 5, 4, 8, 2, 5, 1, 2, 3, 3, 6, 9, 6, 4, 0, 1, 1, 0, 6, 2, 4, 0, 2, 2, 9, 6, 6, 8, 6, 6, 4, 7, 6, 6, 7, 6, 8
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OFFSET

1,1


COMMENTS

See A199597 for a guide to related sequences. The Mathematica program includes a graph.


LINKS

Table of n, a(n) for n=1..99.


EXAMPLE

least: 0.5973392503648539750049736135997669028331...
greatest: 3.0481385953651166891446050593739052208...


MATHEMATICA

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, 2, 4}, {AxesOrigin > {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .6, .5}, WorkingPrecision > 110]
RealDigits[r] (* A199607, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision > 110]
RealDigits[r] (* A199708, greatest of 4 roots *)


CROSSREFS

Cf. A199597.
Sequence in context: A210878 A320373 A303274 * A128178 A255504 A178593
Adjacent sequences: A199605 A199606 A199607 * A199609 A199610 A199611


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Nov 08 2011


STATUS

approved



