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A199152 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=1.

%I A199152 #8 Feb 07 2025 16:44:05
%S A199152 9,3,1,9,4,4,5,3,9,1,9,6,5,7,4,8,0,8,7,5,7,9,9,4,8,2,2,2,1,9,0,3,5,7,
%T A199152 7,7,4,3,2,4,1,6,3,2,3,9,2,4,2,2,3,1,3,6,1,2,1,0,2,9,6,0,5,1,6,3,7,4,
%U A199152 3,3,6,3,4,4,7,8,0,9,1,8,6,6,5,1,4,5,5,7,1,6,5,7,7,3,9,3,4,5,5
%N A199152 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=1.
%C A199152 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199152 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199152 negative: -0.93194453919657480875799482221903577743...
%e A199152 positive:  0.33648270192335281577039493761106778144...
%t A199152 a = 3; b = 2; c = 1;
%t A199152 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199152 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199152 r = x /. FindRoot[f[x] == g[x], {x, -.94, -.93}, WorkingPrecision -> 110]
%t A199152 RealDigits[r]  (* A199152 *)
%t A199152 r = x /. FindRoot[f[x] == g[x], {x, .33, .34}, WorkingPrecision -> 110]
%t A199152 RealDigits[r]  (* A199153 *)
%Y A199152 Cf. A198866.
%K A199152 nonn,cons
%O A199152 0,1
%A A199152 _Clark Kimberling_, Nov 03 2011