A198128 Decimal expansion of greatest x having 2*x^2+3x=cos(x).

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

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: -1.51753898066148224483274698639081150...
greatest x: 0.2718318518958059071868820333588397...

Mathematica

a = 2; b = 3; c = 1;
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, -1.52, -1.51}, WorkingPrecision -> 110]
RealDigits[r1](* A198128 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
RealDigits[r2](* A198129 *)

Prog

(PARI) solve(x=0, 1, 2*x^2+3*x-cos(x)) \\ Charles R Greathouse IV, Apr 14 2026

Crossrefs

Cf. A197737.

Sequence in context: A248685 A182587 A248677 * A094121 A105178 A282171

Adjacent sequences: A198125 A198126 A198127 * A198129 A198130 A198131

Keyword

nonn,cons

Author

Clark Kimberling, Oct 22 2011

Extensions

Name and offset corrected by Charles R Greathouse IV, Apr 14 2026

Status

approved