cp's OEIS Frontend

A200225 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 3*sin(x), negated.

%I A200225 #13 Feb 12 2025 13:03:04
%S A200225 2,5,8,3,7,5,8,6,0,0,8,3,4,8,6,9,4,8,5,9,8,4,3,8,2,6,1,2,2,9,7,3,3,0,
%T A200225 9,2,9,7,5,3,9,3,8,6,9,2,8,8,7,3,0,8,4,4,2,5,8,4,9,6,2,5,0,9,9,9,8,6,
%U A200225 0,7,4,8,4,6,5,9,9,3,6,8,5,2,5,8,6,9,6,6,4,7,7,0,7,6,1,3,9,8,4
%N A200225 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 3*sin(x), negated.
%C A200225 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200225 G. C. Greubel, <a href="/A200225/b200225.txt">Table of n, a(n) for n = 0..10000</a>
%H A200225 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200225 least x: -0.25837586008348694859843826122973...
%e A200225 greatest x: 1.012265562969209417334554419938...
%t A200225 a = 3; b = -1; c = 3;
%t A200225 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200225 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200225 r = x /. FindRoot[f[x] == g[x], {x, -.26, -.25}, WorkingPrecision -> 110]
%t A200225 RealDigits[r]   (* A200225 *)
%t A200225 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200225 RealDigits[r]   (* A200226 *)
%o A200225 (PARI) a=3; b=-1; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018
%Y A200225 Cf. A199949.
%K A200225 nonn,cons
%O A200225 0,1
%A A200225 _Clark Kimberling_, Nov 14 2011