A199616 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=2*sin(x).

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

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

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 *)

Crossrefs

Cf. A199597.

Sequence in context: A378025 A155526 A076553 * A173973 A344076 A333336

Adjacent sequences: A199613 A199614 A199615 * A199617 A199618 A199619

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved