A199171 Decimal expansion of x>0 satisfying x^2+x*cos(x)=1.

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers.

Example

negative: -1.19835984451866026826502160343030898927268...
positive:  0.685174133854503187895211530638458709591...

Mathematica

a = 1; b = 1; 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, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199170 *)
r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]
RealDigits[r]  (* A199171 *)

Crossrefs

Cf. A199170.

Sequence in context: A123092 A209283 A209285 * A323737 A374883 A350860

Adjacent sequences: A199168 A199169 A199170 * A199172 A199173 A199174

Keyword

nonn,cons

Author

Clark Kimberling, Nov 03 2011

Status

approved