A200095 - OEIS

%I #13 Feb 12 2025 09:53:22

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

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

%U 3,8,3,8,7,6,2,7,8,4,0,3,8,9,9,8,9,8,2,7,3,9,2,3,4,8,4,8,2,9,5

%N Decimal expansion of least x satisfying x^2 - 3*cos(x) = 3*sin(x), negated.

%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200095/b200095.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least x:  -0.677119411697943130184179520098917021...

%e greatest x: 1.6546997822939010711316866818308006354...

%t a = 1; b = -3; c = 3;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.88, -.67}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200095 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.65, 1.66}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200096 *)

%o (PARI) a=1; b=-3; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 13 2011