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A199068 Decimal expansion of x > 0 satisfying 2*x^2+2*sin(x) = 1.

%I A199068 #10 Feb 07 2025 16:44:05
%S A199068 3,7,0,8,8,7,3,4,0,1,1,1,9,9,2,0,7,0,6,0,1,4,2,9,3,4,5,7,3,4,4,8,8,9,
%T A199068 9,2,9,4,8,9,9,8,3,1,9,9,9,7,2,7,6,9,5,6,8,7,9,0,7,1,7,0,5,0,6,9,2,0,
%U A199068 6,6,0,3,0,4,2,1,8,8,7,2,5,9,7,7,7,2,4,6,4,4,9,4,1,0,7,7,1,4,6
%N A199068 Decimal expansion of x > 0 satisfying 2*x^2+2*sin(x) = 1.
%C A199068 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199068 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199068 negative: -1.19608203329713481914562195294104321159720...
%e A199068 positive:  0.37088734011199207060142934573448899294899...
%t A199068 a = 2; b = 2; c = 1;
%t A199068 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199068 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199068 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199068 RealDigits[r]  (* A199067 *)
%t A199068 r = x /. FindRoot[f[x] == g[x], {x, .37, .38}, WorkingPrecision -> 110]
%t A199068 RealDigits[r]  (* A199068 *)
%Y A199068 Cf. A198866.
%K A199068 nonn,cons
%O A199068 0,1
%A A199068 _Clark Kimberling_, Nov 02 2011
%E A199068 a(82) onwards corrected by _Georg Fischer_, Aug 01 2021