A197815 Decimal expansion of least x having x^2-2x=-cos(x).

5, 8, 9, 3, 0, 3, 2, 0, 8, 1, 5, 9, 0, 1, 2, 8, 7, 4, 7, 2, 5, 2, 2, 3, 9, 1, 9, 0, 7, 3, 8, 6, 9, 1, 8, 5, 8, 8, 9, 0, 6, 0, 9, 8, 8, 0, 5, 4, 0, 7, 0, 3, 0, 5, 5, 3, 9, 2, 1, 4, 0, 7, 5, 1, 1, 7, 1, 4, 5, 7, 1, 7, 7, 0, 6, 4, 7, 2, 4, 1, 0, 8, 8, 0, 5, 2, 2, 1, 0, 2, 0, 0, 1, 6, 9, 6, 5, 6, 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: 0.589303208159012874725223919073869185889...
greatest x: 2.287086177656584485337033312314491737...

Mathematica

a = 1; b = -2; c = -1;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 3}]
r1 = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
RealDigits[r1] (* A197815 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
RealDigits[r2] (* A197820  *)

Prog

(PARI) solve(x=.5, .6, x^2-2*x+cos(x)) \\ Charles R Greathouse IV, Apr 19 2026

Crossrefs

Cf. A197737.

Sequence in context: A241992 A263176 A378207 * A257870 A388931 A338275

Adjacent sequences: A197812 A197813 A197814 * A197816 A197817 A197818

Keyword

nonn,cons

Author

Clark Kimberling, Oct 20 2011

Status

approved