A198140 Decimal expansion of least x having x^2-2x=-3*cos(x). Decimal expansion of greatest x having x^2-2x=-3*cos(x).

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

Offset

1,2

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Links

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

Example

least x: 1.25361062916653958630784246694528362...
greatest x: 2.99155642389786356257272264824822031...

Mathematica

a = 1; b = -2; c = -3;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 4}]
r1 = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
RealDigits[r1] (* A198140 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r2] (* A198141 *)

Crossrefs

Cf. A197737.

Sequence in context: A124568 A091807 A085825 * A339259 A340066 A212614

Adjacent sequences: A198137 A198138 A198139 * A198141 A198142 A198143

Keyword

nonn,cons

Author

Clark Kimberling, Oct 21 2011

Status

approved