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A199291 Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 1.

%I A199291 #13 Feb 07 2025 16:44:05
%S A199291 9,4,2,0,1,3,1,7,1,7,4,5,9,2,5,4,7,0,2,7,8,3,8,5,4,7,8,8,1,6,3,3,3,9,
%T A199291 0,3,0,6,4,8,6,9,2,9,1,2,9,9,0,4,0,5,4,1,8,0,5,3,8,2,4,1,4,7,3,2,3,5,
%U A199291 1,2,6,9,1,1,5,1,8,2,2,1,7,9,0,8,7,1,5,2,9,8,1,8,3,3,2,5,2,7,2,5,5,9,5
%N A199291 Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 1.
%C A199291 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199291 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199291 negative: -0.942013171745925470278385478816333...
%e A199291 positive:  0.2701502896318032580209778461269860...
%t A199291 a = 3; b = 3; c = 1;
%t A199291 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199291 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199291 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199291 RealDigits[r]     (* A199291 *)
%t A199291 r = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
%t A199291 RealDigits[r]    (* A199292 *)
%Y A199291 Cf. A199170, A199292.
%K A199291 nonn,cons
%O A199291 0,1
%A A199291 _Clark Kimberling_, Nov 05 2011
%E A199291 a(92) onwards corrected by _Georg Fischer_, Aug 03 2021