A199187 Decimal expansion of x>0 satisfying x^2+3*x*cos(x)=3.

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

Offset

1,1

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

negative: -1.6364435519550414220675930311871282455...
positive:  3.56968633396230393049792896687800143343...

Mathematica

a = 1; b = 3; c = 3;
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}}]
Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199186 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.56, 3.57}, WorkingPrecision -> 110]
RealDigits[r]  (*  A199187 *)

Crossrefs

Cf. A199170.

Sequence in context: A199730 A016612 A245739 * A098587 A321885 A161182

Adjacent sequences: A199184 A199185 A199186 * A199188 A199189 A199190

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Status

approved