

A199182


Decimal expansion of least x satisfying x^2+3*x*cos(x)=1.


4



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

1,2


COMMENTS

See A199170 for a guide to related sequences. The Mathematica program includes a graph.


LINKS

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


EXAMPLE

least: 1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...


MATHEMATICA

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, 2 Pi, 2 Pi}, {AxesOrigin > {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.3}, WorkingPrecision > 110]
RealDigits[r] (* A199182 least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision > 110]
RealDigits[r] (* A199183 greatest of four roots *)


CROSSREFS

Cf. A199170.
Sequence in context: A010470 A181916 A077590 * A011368 A020811 A200005
Adjacent sequences: A199179 A199180 A199181 * A199183 A199184 A199185


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Nov 04 2011


STATUS

approved



