A200022 - OEIS

%I #11 Jun 24 2018 21:38:46

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

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

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

%N Decimal expansion of least x satisfying x^2 - 2*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="/A200022/b200022.txt">Table of n, a(n) for n = 0..10000</a>

%e least x:  -0.5145148304764586865656389456753718159521...

%e greatest x: 1.669692169649763458252838305984917335937...

%t a = 1; b = -2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.52, -.51}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200022 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.66, 1.67}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200023 *)

%o (PARI) a=1; b=-2; 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