A199292 Decimal expansion of x>0 satisfying 3*x^2+3*x*cos(x)=1.

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

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: -0.942013171745925470278385478816333...
positive:  0.2701502896318032580209778461269860...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

Mathematica

a = 3; b = 3; 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, -.9}, WorkingPrecision -> 110]
RealDigits[r]     (* A199291 *)
r = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
RealDigits[r]    (* A199292 *)