A198228 Decimal expansion of least x having 3*x^2+2x=4*cos(x), negated.

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

Offset

1,3

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.

Index entries for transcendental numbers.

Example

least x: -1.146069580210441813394351195780611...
greatest x: 0.721341307648015582421031722872306448...

Mathematica

a = 3; b = 2; c = 4;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r1] (* A198228 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .72, .73}, WorkingPrecision -> 110]
RealDigits[r2] (* A198229 *)

Prog

(PARI) solve(x=-2, -1, 3*x^2+2*x-4*cos(x)) \\ Charles R Greathouse IV, Apr 15 2026

Crossrefs

Cf. A197737.

Sequence in context: A194183 A011442 A135183 * A200349 A021221 A197006

Adjacent sequences: A198225 A198226 A198227 * A198229 A198230 A198231

Keyword

nonn,cons

Author

Clark Kimberling, Oct 23 2011

Status

approved