cp's OEIS Frontend

A200277 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = sin(x), negated.

%I A200277 #16 Feb 12 2025 13:08:54
%S A200277 8,1,7,7,1,5,2,1,8,7,9,2,3,0,4,5,4,5,1,1,1,9,1,4,5,4,2,0,8,3,6,5,7,7,
%T A200277 7,1,5,3,9,3,9,1,6,5,1,3,2,7,1,2,0,1,5,3,7,2,7,9,0,7,5,0,9,9,8,6,2,4,
%U A200277 1,4,4,1,9,7,2,7,4,5,8,0,2,7,4,7,1,3,8,1,9,8,3,6,2,7,8,7,2,9,0
%N A200277 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = sin(x), negated.
%C A200277 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200277 G. C. Greubel, <a href="/A200277/b200277.txt">Table of n, a(n) for n = 0..10000</a>
%H A200277 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200277 least x: -0.81771521879230454511191454208365777...
%e A200277 greatest x: 1.000303639283590185187225035744180...
%t A200277 a = 3; b = -4; c = 1;
%t A200277 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200277 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200277 r = x /.  FindRoot[f[x] == g[x], {x, -.82, -.81}, WorkingPrecision -> 110]
%t A200277 RealDigits[r]   (* A200277  *)
%t A200277 r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
%t A200277 RealDigits[r]   (* A200278 *)
%o A200277 (PARI) a=3; b=-4; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y A200277 Cf. A199949.
%K A200277 nonn,cons
%O A200277 0,1
%A A200277 _Clark Kimberling_, Nov 15 2011