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A199059 Decimal expansion of x > 0 satisfying x^2+3*sin(x) = 3.

%I A199059 #10 Feb 07 2025 16:44:05
%S A199059 8,5,6,4,3,0,5,5,5,9,0,7,5,6,1,1,7,9,4,6,3,6,3,2,5,3,8,7,5,2,4,8,2,9,
%T A199059 7,6,0,9,8,9,3,9,8,2,3,9,7,2,4,3,4,5,1,5,7,3,3,8,4,1,3,9,9,3,0,5,3,9,
%U A199059 4,8,8,2,7,0,6,6,5,1,9,3,8,7,2,9,7,0,9,8,5,0,5,1,4,3,8,2,6,5,9
%N A199059 Decimal expansion of x > 0 satisfying x^2+3*sin(x) = 3.
%C A199059 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199059 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199059 negative: -2.2919650412674286490951331183944433...
%e A199059 positive:  0.8564305559075611794636325387524829760...
%t A199059 a = 1; b = 3; c = 3;
%t A199059 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199059 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A199059 r = x /. FindRoot[f[x] == g[x], {x, -2.3, -2.2}, WorkingPrecision -> 110]
%t A199059 RealDigits[r]  (* A199058 *)
%t A199059 r = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]
%t A199059 RealDigits[r] (* A199059 *)
%Y A199059 Cf. A198866.
%K A199059 nonn,cons
%O A199059 0,1
%A A199059 _Clark Kimberling_, Nov 02 2011
%E A199059 a(97), a(98) corrected by _Georg Fischer_, Aug 01 2021