A199741 Decimal expansion of x>0 satisfying 2*x^2-x*cos(x)=2*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 10 2011

Keywords

• nonn
• cons

Comments

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			1.0642302228710730261002141143294370961885395132859...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 2; b = -1; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.06, 1.07}, WorkingPrecision -> 110]
RealDigits[r]   (* A199741 *)

Extensions

Name corrected by Sean A. Irvine, Jan 12 2025