A199867 Decimal expansion of x > 0 satisfying 4*x^2 - 2*x*cos(x) = sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 11 2011

Keywords

• nonn
• cons

Comments

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

Examples

			0.63579423397192655143542664210015922323...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 4; b = -2; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .63, .64}, WorkingPrecision -> 110]
RealDigits[r]    (* A199867 *)

Extensions

a(90) onwards corrected by Georg Fischer, Aug 03 2021