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A199151 Decimal expansion of x>0 satisfying 3*x^2+sin(x)=3.

%I A199151 #8 Feb 07 2025 16:44:05
%S A199151 8,6,4,0,1,1,2,7,2,4,2,7,9,0,3,4,5,7,3,2,9,5,5,0,3,1,5,0,3,5,9,0,0,2,
%T A199151 9,4,7,0,4,8,8,0,1,7,2,7,8,9,4,2,0,3,8,5,2,7,5,0,0,7,7,8,3,4,3,8,2,4,
%U A199151 2,2,0,4,0,1,2,5,9,8,3,2,0,0,5,6,4,3,1,1,8,0,0,8,8,7,4,2,1,7,8
%N A199151 Decimal expansion of x>0 satisfying 3*x^2+sin(x)=3.
%C A199151 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199151 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199151 negative: -1.1415298646423925627075066056294867784...
%e A199151 positive:  0.86401127242790345732955031503590029470...
%t A199151 a = 3; b = 1; c = 3;
%t A199151 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199151 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199151 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199151 RealDigits[r]   (* A199150 *)
%t A199151 r = x /. FindRoot[f[x] == g[x], {x, .86, .87}, WorkingPrecision -> 110]
%t A199151 RealDigits[r]   (* A199151 *)
%Y A199151 Cf. A198866.
%K A199151 nonn,cons
%O A199151 0,1
%A A199151 _Clark Kimberling_, Nov 03 2011