A198942 Decimal expansion of x>0 satisfying 3*x^2-4*cos(x)=4.

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

Offset: 1

Author

Clark Kimberling, Nov 01 2011

Keywords

• nonn
• cons

Comments

Distance from x to 13/10 is < 1/10^6.

See A198755 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			1.2999995979570405341847932770591791399959...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A198755.

Programs

Mathematica

a = 3; b = -4; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.29, 1.3}, WorkingPrecision -> 110]
RealDigits[r] (* A198942 *)