A198991 Decimal expansion of x>0 satisfying 4*x^2-2*cos(x)=-1.

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

Offset: 0

Author

Clark Kimberling, Nov 01 2011

Keywords

• nonn
• cons

Comments

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

Examples

			0.44795830764740687230976418404518540235389753...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A198755.

Programs

Maple

Digits:=100: fsolve(4*x^2-2*cos(x)=-1,x); # Wesley Ivan Hurt, Feb 09 2017

Mathematica

a = 4; b = -2; c = -1;
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, .44, .45}, WorkingPrecision -> 110]
RealDigits[r] (* A198991 *)

PARI

solve(x=0, 1, 4*x^2 - 2*cos(x) + 1) \\ Michel Marcus, Feb 09 2017