cp's OEIS Frontend

A199288 Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=2.

%I A199288 #8 Feb 07 2025 16:44:05
%S A199288 5,8,4,5,3,2,4,9,0,7,9,0,4,0,6,3,0,4,5,3,3,6,9,6,6,4,0,0,1,1,1,7,9,3,
%T A199288 3,7,1,1,3,1,3,9,0,9,0,0,5,1,8,3,4,6,3,7,3,0,5,7,6,4,4,5,2,8,6,3,8,7,
%U A199288 6,3,9,6,3,3,7,4,7,9,4,2,2,9,4,7,5,9,2,2,1,3,1,0,8,2,4,3,4,7,7
%N A199288 Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=2.
%C A199288 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199288 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199288 negative: -1.01209273887228943407465426872436881...
%e A199288 positive:  0.584532490790406304533696640011179337...
%t A199288 a = 3; b = 2; c = 2;
%t A199288 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199288 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199288 r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1}, WorkingPrecision -> 110]
%t A199288 RealDigits[r]    (* A199287 *)
%t A199288 r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t A199288 RealDigits[r]    (* A199288 *)
%Y A199288 Cf. A199170.
%K A199288 nonn,cons
%O A199288 0,1
%A A199288 _Clark Kimberling_, Nov 05 2011