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A199067 Decimal expansion of x < 0 satisfying 2*x^2+2*sin(x) = 1.

%I A199067 #10 Feb 07 2025 16:44:05
%S A199067 1,1,9,6,0,8,2,0,3,3,2,9,7,1,3,4,8,1,9,1,4,5,6,2,1,9,5,2,9,4,1,0,4,3,
%T A199067 2,1,1,5,9,7,2,0,4,7,1,5,9,5,9,6,8,3,8,0,5,1,0,2,3,8,0,7,4,0,4,9,8,1,
%U A199067 6,1,1,3,2,3,3,5,5,1,9,8,2,1,9,3,1,4,3,5,8,7,7,9,5,7,3,7,8,6,2,5
%N A199067 Decimal expansion of x < 0 satisfying 2*x^2+2*sin(x) = 1.
%C A199067 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199067 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199067 negative: -1.19608203329713481914562195294104321159720...
%e A199067 positive:  0.37088734011199207060142934573448899294899...
%t A199067 a = 2; b = 2; c = 1;
%t A199067 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199067 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199067 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199067 RealDigits[r]  (* A199067 *)
%t A199067 r = x /. FindRoot[f[x] == g[x], {x, .37, .38}, WorkingPrecision -> 110]
%t A199067 RealDigits[r]  (* A199068 *)
%Y A199067 Cf. A198866.
%K A199067 nonn,cons
%O A199067 1,3
%A A199067 _Clark Kimberling_, Nov 02 2011
%E A199067 a(92) onwards corrected by _Georg Fischer_, Aug 01 2021