A199959 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 3*sin(x).

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

Offset

1,3

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

least x:  1.046472542540093403618073553786437093400...
greatest x: 1.9905034616684938355818760222044124763...

Mathematica

a = 1; b = 3; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A199959 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.99, 2.0}, WorkingPrecision -> 110]
RealDigits[r]   (* A199960 *)

Prog

(PARI) a=1; b=3; c=3; solve(x=1, 1.5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

Crossrefs

Cf. A199949.

Sequence in context: A083396 A142973 A181110 * A084892 A344475 A245556

Adjacent sequences: A199956 A199957 A199958 * A199960 A199961 A199962

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved