A199175 Decimal expansion of x>0 satisfying x^2+x*cos(x)=3.

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

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

negative: -1.67892976349109451959338320116343299...
positive:  1.90253038503823570345779582773972676...

Mathematica

a = 1; b = 1; 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}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A199174 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.90, 1.91}, WorkingPrecision -> 110]
RealDigits[r]  (* A199175 *)

Crossrefs

Cf. A199170.

Sequence in context: A198556 A261169 A093767 * A261313 A203129 A107091

Adjacent sequences: A199172 A199173 A199174 * A199176 A199177 A199178

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Status

approved