A200285 - OEIS

%I #12 Feb 12 2025 14:33:53

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

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

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

%N Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x), negated.

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

%H G. C. Greubel, <a href="/A200285/b200285.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: -0.37540364996113984869295773583715442...

%e greatest x: 0.588851742675041179999659714644848...

%t a = 4; b = -1; c = 1;

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

%t Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200285 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200286 *)

%o (PARI) a=4; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011