A199615 Decimal expansion of least x satisfying x^2 + 4*x*cos(x) = 2*sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 08 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: -0.856374049744346109322078062564729199476600...
greatest:  3.515613199687358023842180210704030792217...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
RealDigits[r]  (* A199615, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199616, greatest of 4 roots *)

Extensions

a(96) onwards corrected by Georg Fischer, Aug 03 2021