A199290 Decimal expansion of x > 0 satisfying 3*x^2 + 2*x*cos(x) = 3.

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

Offset: 0

Author

Clark Kimberling, Nov 05 2011

Keywords

• nonn
• cons

Comments

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

Examples

			negative: -1.1465729939312446659051094914162065825...
positive:  0.79310716512209201308469669867166689386...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170, A199289.

Programs

Mathematica

a = 3; b = 2; c = 3;
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, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r]    (* A199289 *)
r = x /. FindRoot[f[x] == g[x], {x, .79, .80}, WorkingPrecision -> 110]
RealDigits[r]    (* A199290 *)

Extensions

a(86) onwards corrected by Georg Fischer, Aug 03 2021