A199270 Decimal expansion of x > 0 satisfying 2*x^2 + 2*x*cos(x) = 1.

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

Example

negative: -1.017240798342455566560350070545346176017411...
positive:  0.381748420992985957918521611823486645593341...

Mathematica

a = 2; b = 2; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
RealDigits[r]   (* A199269 *)
r = x /. FindRoot[f[x] == g[x], {x, .38, .39}, WorkingPrecision -> 110]
RealDigits[r]   (* A199270 *)

Crossrefs

Cf. A199170, A199269.

Sequence in context: A021266 A054399 A013676 * A131563 A016622 A143623

Adjacent sequences: A199267 A199268 A199269 * A199271 A199272 A199273

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Extensions

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

Status

approved