A199269 Decimal expansion of x<0 satisfying 2*x^2+2*x*cos(x)=1.

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

Offset: 1

Author

Clark Kimberling, Nov 04 2011

Keywords

• nonn
• cons

Comments

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

Examples

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

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

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 *)