A199188 Decimal expansion of x < 0 satisfying 2*x^2+x*cos(x) = 1.

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

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: -0.883330197195891938925896450885677107...
positive:  0.522945946113111737247623836359811237...

Mathematica

a = 2; b = 1; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.84, -.83}, WorkingPrecision -> 110]
RealDigits[r]  (* A199188 *)
r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]
RealDigits[r]  (*  A199189 *)

Crossrefs

Cf. A199170.

Sequence in context: A289915 A021535 A371466 * A340552 A254291 A219300

Adjacent sequences: A199185 A199186 A199187 * A199189 A199190 A199191

Keyword

nonn,cons

Author

Clark Kimberling, Nov 04 2011

Extensions

Offset corrected by Georg Fischer, Aug 02 2021

Status

approved