A197810 Decimal expansion of x>0 having x^2+x=2*cos(x).

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

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

negative: -1.3405253081973984478676062849960660920583...
positive:  0.7883968459929654290788209839820019122955...

Mathematica

a = 1; b = 1; c = 2;
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, -1.3}, WorkingPrecision -> 110]
RealDigits[r1] (* A197809 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .78, .79}, WorkingPrecision -> 110]
RealDigits[r2] (* A197810 *)

Prog

(PARI) solve(x=.7, .8, x^2+x-2*cos(x)) \\ Charles R Greathouse IV, May 17 2026

Crossrefs

Cf. A197737.

Sequence in context: A065470 A353781 A338815 * A085361 A256781 A248224

Adjacent sequences: A197807 A197808 A197809 * A197811 A197812 A197813

Keyword

nonn,cons

Author

Clark Kimberling, Oct 20 2011

Status

approved