A199738 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=sin(x).

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

Offset

1,2

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: -3.6417365104232030891568017121916889194744...
greatest:  1.39694868354568477235286357946526821398...

Mathematica

a = 1; b = -4; c = 1;
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, -3.7, -3.6}, WorkingPrecision -> 110]
RealDigits[r]   (* A199737 least root *)
r = x /. FindRoot[f[x] == g[x], {x, 1.39, 1.40}, WorkingPrecision -> 110]
RealDigits[r]   (* A199738 greatest root *)

Crossrefs

Cf. A199597.

Sequence in context: A021256 A349850 A331063 * A343864 A309613 A189272

Adjacent sequences: A199735 A199736 A199737 * A199739 A199740 A199741

Keyword

nonn,cons

Author

Clark Kimberling, Nov 09 2011

Status

approved