cp's OEIS Frontend

A200114 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 4*sin(x), negated.

%I A200114 #12 Feb 12 2025 11:22:02
%S A200114 2,2,1,2,3,4,7,1,6,8,5,6,5,5,0,8,4,5,9,2,8,7,5,1,6,1,4,5,6,5,1,7,9,1,
%T A200114 5,6,6,1,6,0,0,1,8,4,8,1,0,3,7,5,1,2,2,6,1,0,9,7,5,6,4,8,7,2,2,1,3,6,
%U A200114 8,0,3,2,0,7,6,1,3,9,5,9,6,8,0,3,8,5,5,3,6,8,5,1,5,0,2,9,7,5,8
%N A200114 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 4*sin(x), negated.
%C A200114 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200114 G. C. Greubel, <a href="/A200114/b200114.txt">Table of n, a(n) for n = 0..10000</a>
%H A200114 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200114 least x: -0.22123471685655084592875161456517915661...
%e A200114 greatest x: 1.431778732687231131820591799700558843...
%t A200114 a = 2; b = -1; c = 4;
%t A200114 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200114 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200114 r = x /. FindRoot[f[x] == g[x], {x, -.23, -.22}, WorkingPrecision -> 110]
%t A200114 RealDigits[r]  (* A200114 *)
%t A200114 r = x /. FindRoot[f[x] == g[x], {x, 1.43, 1.44}, WorkingPrecision -> 110]
%t A200114 RealDigits[r]  (* A200115 *)
%o A200114 (PARI) a=2; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 29 2018
%Y A200114 Cf. A199949.
%K A200114 nonn,cons
%O A200114 0,1
%A A200114 _Clark Kimberling_, Nov 13 2011