A197814 Decimal expansion of x>0 having x^2+x=4*cos(x).

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

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

negative: -1.42077677317100524932506694166184882...
positive: 1.025119111992429014846198575005783251...

Mathematica

a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1.5}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]
RealDigits[r1] (* A197813 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 1, 1.1}, WorkingPrecision -> 110]
RealDigits[r2] (* A197814 *)

Prog

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

Crossrefs

Cf. A197737.

Sequence in context: A376316 A197737 A189824 * A091772 A275479 A075790

Adjacent sequences: A197811 A197812 A197813 * A197815 A197816 A197817

Keyword

nonn,cons

Author

Clark Kimberling, Oct 20 2011

Status

approved