A200129 Decimal expansion of greatest x satisfying 2*x^2 - 4*cos(x) = sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 14 2011

Keywords

• nonn
• cons

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -0.91125136577248241254947318280293...
greatest x: 1.13740119952686852650278803084...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 2; b = -4; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.92, -.91}, WorkingPrecision -> 110]
RealDigits[r]  (* A200128 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.13, 1.14}, WorkingPrecision -> 110]
RealDigits[r]  (* A200129 *)

PARI

a=2; b=-4; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 01 2018