A200099 - OEIS

%I #13 Feb 12 2025 09:54:21

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

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

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

%N Decimal expansion of least x satisfying x^2 - 4*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="/A200099/b200099.txt">Table of n, a(n) for n = 1..10000</a>

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

%e least x:  -1.053352983600153733281110157999...

%e greatest x: 1.35457555821585784490890770164646...

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

%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, -1.06, -1.05}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200099 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.35, 1.36}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200100 *)

%o (PARI) a=1; b=-4; c=1; solve(x=-2, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 13 2011