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A198932 Decimal expansion of x>0 satisfying 3*x^2-3*cos(x)=-1.

%I A198932 #8 Feb 07 2025 17:52:29
%S A198932 6,7,0,8,0,9,5,0,1,1,9,2,0,7,4,3,9,7,2,6,1,1,5,6,3,7,8,3,9,2,4,7,4,2,
%T A198932 2,6,0,1,5,6,7,0,7,0,9,9,2,3,1,1,4,7,2,2,8,9,5,4,0,4,7,7,1,7,3,0,2,1,
%U A198932 0,1,9,9,4,4,4,0,3,2,3,8,9,5,7,8,1,1,3,7,6,7,8,7,6,8,5,9,5,0,9
%N A198932 Decimal expansion of x>0 satisfying 3*x^2-3*cos(x)=-1.
%C A198932 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198932 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198932 0.670809501192074397261156378392474226015...
%t A198932 a = 3; b = -3; c = -1;
%t A198932 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198932 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198932 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A198932 RealDigits[r] (* A198932 *)
%Y A198932 Cf. A198755.
%K A198932 nonn,cons
%O A198932 0,1
%A A198932 _Clark Kimberling_, Oct 31 2011