A199177 Decimal expansion of x>0 satisfying x^2+2*x*cos(x)=1.

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

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.

Example

negative: -1.301201733141911400798397364440264522...
positive:  0.444416809391791633213083601823107078...

Mathematica

a = 1; b = 2; 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]  (* A199176 *)
r = x /. FindRoot[f[x] == g[x], {x, .44, .45}, WorkingPrecision -> 110]
RealDigits[r]  (* A199177 *)

Crossrefs

Cf. A199170.

Sequence in context: A071907 A172369 A190338 * A320086 A074803 A177229

Adjacent sequences: A199174 A199175 A199176 * A199178 A199179 A199180

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Status

approved