A199733 Decimal expansion of least x satisfying x^2-4*x*cos(x)=3*sin(x).

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..99.

Example

least: -3.746168565528221340687013560527596978856...
greatest:  1.625278383378448643933003226246836106...

Mathematica

a = 1; b = -4; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199733 least root *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199734 greatest root *)

Crossrefs

Cf. A199597.

Sequence in context: A238274 A094689 A019831 * A193625 A198886 A305202

Adjacent sequences: A199730 A199731 A199732 * A199734 A199735 A199736

Keyword

nonn,cons

Author

Clark Kimberling, Nov 09 2011

Status

approved