A199174 Decimal expansion of x < 0 satisfying x^2 + x*cos(x) = 3.

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

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..103.

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, A199175.

Sequence in context: A308147 A308165 A090928 * A335094 A153604 A324031

Adjacent sequences: A199171 A199172 A199173 * A199175 A199176 A199177

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Extensions

a(84) onwards corrected by Georg Fischer, Aug 03 2021

Status

approved