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A199048 Decimal expansion of x < 0 satisfying x^2 + sin(x) = 3.

%I A199048 #15 Feb 07 2025 16:44:05
%S A199048 1,9,7,9,3,2,0,1,4,6,5,5,6,2,1,1,4,6,0,3,3,5,7,4,9,7,1,3,9,8,8,4,7,4,
%T A199048 4,5,2,1,1,6,6,4,2,1,5,0,5,9,4,1,8,4,6,6,7,9,1,4,0,9,7,5,5,5,8,1,8,1,
%U A199048 1,9,5,8,4,1,9,3,2,6,5,0,0,7,5,5,1,5,8,8,0,8,8,6,6,3,9,3,3,1,6
%N A199048 Decimal expansion of x < 0 satisfying x^2 + sin(x) = 3.
%C A199048 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199048 G. C. Greubel, <a href="/A199048/b199048.txt">Table of n, a(n) for n = 1..10000</a>
%H A199048 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199048 negative: -1.979320146556211460335749713988...
%e A199048 positive:  1.4183100916225250456919496008037...
%t A199048 a = 1; b = 1; c = 3;
%t A199048 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199048 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A199048 r = x /. FindRoot[f[x] == g[x], {x, -1.98, -1.97}, WorkingPrecision -> 110]
%t A199048 RealDigits[r] (* this sequence *)
%t A199048 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A199048 RealDigits[r] (* A199049 *)
%o A199048 (PARI) a=1; b=1; c=3; solve(x=-2, 0, a*x^2 - c + b*sin(x)) \\ _G. C. Greubel_, Feb 19 2019
%o A199048 (Sage) a=1; b=1; c=3; (a*x^2 + b*sin(x)==c).find_root(-2,0,x) # _G. C. Greubel_, Feb 19 2019
%Y A199048 Cf. A198866, A199049.
%K A199048 nonn,cons
%O A199048 1,2
%A A199048 _Clark Kimberling_, Nov 02 2011