A198227 Decimal expansion of least x having 3*x^2+2x=3*cos(x), negated. Decimal expansion of greatest x having 3*x^2-2x=3*cos(x).

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Index entries for transcendental numbers.

Example

least x: -1.0904382560388744089252035126068065372...
greatest x: 0.626466337849291863012350106335876205...

Mathematica

a = 3; b = 2; c = 3;
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, -1.1, -1.08}, WorkingPrecision -> 110]
RealDigits[r1] (* A198226 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .62, .63}, WorkingPrecision -> 110]
RealDigits[r2] (* A198227 *)

Prog

(PARI) solve(x=1, 2, 3*x^2-2*x-3*cos(x)) \\ Charles R Greathouse IV, Apr 19 2026

Crossrefs

Cf. A197737.

Sequence in context: A266389 A198986 A236190 * A199505 A241033 A216992

Adjacent sequences: A198224 A198225 A198226 * A198228 A198229 A198230

Keyword

nonn,cons

Author

Clark Kimberling, Oct 23 2011

Extensions

Name corrected by Charles R Greathouse IV, Apr 19 2026

Status

approved