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A199052 Decimal expansion of least x satisfying x^2+3*sin(x)=-1.

%I A199052 #10 Feb 07 2025 16:44:05
%S A199052 1,3,9,8,4,0,3,0,6,8,9,5,6,7,0,4,2,8,1,9,1,3,6,2,1,0,7,0,1,0,0,3,3,0,
%T A199052 8,6,9,9,2,9,2,5,4,1,2,5,1,2,3,2,2,0,9,0,4,8,2,2,7,3,3,7,6,6,8,4,7,7,
%U A199052 1,7,9,8,3,3,7,9,6,0,2,2,4,7,0,0,9,9,0,4,2,9,7,8,1,0,5,1,9,4,2
%N A199052 Decimal expansion of least x satisfying x^2+3*sin(x)=-1.
%C A199052 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199052 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199052 least: -1.39840306895670428191362107010033086...
%e A199052 greatest:  -0.3958092344691378375825479943405218925...
%t A199052 a = 1; b = 3; c = -1;
%t A199052 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199052 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A199052 r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
%t A199052 RealDigits[r] (* A199052 *)
%t A199052 r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
%t A199052 RealDigits[r] (* A199053 *)
%Y A199052 Cf. A198866.
%K A199052 nonn,cons
%O A199052 1,2
%A A199052 _Clark Kimberling_, Nov 02 2011
%E A199052 a(92) onwards corrected by _Georg Fischer_, Aug 01 2021