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A199153 Decimal expansion of x>0 satisfying 3*x^2+2*sin(x)=1.

%I A199153 #8 Feb 07 2025 16:44:05
%S A199153 3,3,6,4,8,2,7,0,1,9,2,3,3,5,2,8,1,5,7,7,0,3,9,4,9,3,7,6,1,1,0,6,7,7,
%T A199153 8,1,4,4,3,6,5,3,0,1,1,7,8,4,0,0,3,6,7,9,4,6,8,5,6,3,5,3,2,4,2,5,3,4,
%U A199153 9,3,1,1,2,9,0,3,6,8,3,7,2,5,6,4,9,3,2,1,7,3,9,8,2,0,0,1,7,2,7
%N A199153 Decimal expansion of x>0 satisfying 3*x^2+2*sin(x)=1.
%C A199153 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199153 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199153 negative: -0.93194453919657480875799482221903577743...
%e A199153 positive:  0.336482701923352815770394937611067781443...
%t A199153 a = 3; b = 2; c = 1;
%t A199153 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199153 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199153 r = x /. FindRoot[f[x] == g[x], {x, -.94, -.93}, WorkingPrecision -> 110]
%t A199153 RealDigits[r]  (* A199152 *)
%t A199153 r = x /. FindRoot[f[x] == g[x], {x, .33, .34}, WorkingPrecision -> 110]
%t A199153 RealDigits[r]  (* A199153 *)
%Y A199153 Cf. A198866.
%K A199153 nonn,cons
%O A199153 0,1
%A A199153 _Clark Kimberling_, Nov 03 2011