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A199505 Decimal expansion of x>0 satisfying 3*x^2-x*sin(x)=cos(x).

%I A199505 #8 Feb 08 2025 10:00:46
%S A199505 6,2,6,4,7,0,1,4,9,1,6,1,3,5,9,1,8,6,5,7,0,2,4,4,2,7,0,7,0,8,7,0,4,2,
%T A199505 8,7,0,5,8,4,7,2,3,7,1,4,2,7,3,9,7,8,8,7,7,5,3,7,3,8,4,2,5,2,9,4,9,7,
%U A199505 3,2,1,3,7,6,9,5,0,4,7,7,4,7,6,3,0,2,5,0,0,1,9,0,7,5,9,5,3,7,9
%N A199505 Decimal expansion of x>0 satisfying 3*x^2-x*sin(x)=cos(x).
%C A199505 See A199429 for a guide to related sequences. The Mathematica program includes a graph.
%H A199505 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199505 0.6264701491613591865702442707087042870584...
%t A199505 a = 3; b = -1; c = 1;
%t A199505 f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
%t A199505 Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t A199505 r = x /. FindRoot[f[x] == g[x], {x, .62, .63}, WorkingPrecision -> 110]
%t A199505 RealDigits[r]  (* A199505 *)
%Y A199505 Cf. A199429.
%K A199505 nonn,cons
%O A199505 0,1
%A A199505 _Clark Kimberling_, Nov 07 2011