A199460 Decimal expansion of x > 0 satisfying x = 2*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 07 2011

Keywords

• nonn
• cons

Comments

See A199429 for a guide to related sequences. The Mathematica program includes a graph.

A solution to the functional equation f'(z) = f(z+1)-f(z-1) is f(z) = exp(x*i*z). - Jean-François Alcover, Apr 04 2014

The solution c of s/c = 2, where s = arclength and c = chord length on the unit circle. - Clark Kimberling, Jul 08 2020

Examples

			1.895494267033980947144035738093601691751...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199429.

Programs

Mathematica

a = 1; b = -2; c = 0;
f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /.  FindRoot[f[x] == g[x], {x, 1.89, 1.90}, WorkingPrecision -> 110]
RealDigits[r]  (* A199460 greatest of three roots *)

Formula

Equals lim_{n->oo} x_n where x_(n+1)=2*sin(x_n). - Christoph B. Kassir, Jun 30 2021