A198216 Decimal expansion of least x having 3*x^2+x=2*cos(x).

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

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: -0.850440081427008538547913177891557825...
greatest x: 0.59486328035771871417159207790102787...

Mathematica

a = 3; b = 1; c = 2;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]
RealDigits[r1]  (* A198216 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .59, .6}, WorkingPrecision -> 110]
RealDigits[r2] (* A198217 *)

Prog

(PARI) solve(x=0, 1, 3*x^2+x-2*cos(x)) \\ Charles R Greathouse IV, Apr 10 2026

Crossrefs

Cf. A197737.

Sequence in context: A154165 A388097 A377695 * A361260 A300074 A096340

Adjacent sequences: A198213 A198214 A198215 * A198217 A198218 A198219

Keyword

nonn,cons

Author

Clark Kimberling, Oct 22 2011

Status

approved