A199775 Decimal expansion of x>0 satisfying 2*x^2 - 2*x*cos(x) = 3*sin(x).

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

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

1.331486959335040503327363069917339543025...

Mathematica

a = 2; b = -2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.33, 1.34}, WorkingPrecision -> 110]
RealDigits[r]   (* A199775 *)

Prog

(PARI) solve(x=1, 2, 2*x^2-2*x*cos(x)-3*sin(x)) \\ Charles R Greathouse IV, Dec 28 2011

Crossrefs

Cf. A199597.

Sequence in context: A298496 A137919 A079081 * A193740 A111408 A327148

Adjacent sequences: A199772 A199773 A199774 * A199776 A199777 A199778

Keyword

nonn,cons

Author

Clark Kimberling, Nov 10 2011

Status

approved