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A199083 Decimal expansion of x>0 satisfying x^2 + 2*sin(x) = 2.

%I A199083 #11 Feb 07 2025 16:44:05
%S A199083 7,7,4,9,8,0,8,1,4,4,2,3,0,4,3,4,4,5,9,5,8,5,9,3,5,0,2,4,7,0,4,0,1,9,
%T A199083 1,4,6,7,6,9,3,8,6,6,1,8,5,6,1,6,3,3,1,0,6,1,5,5,2,5,6,6,3,6,2,3,7,4,
%U A199083 2,3,1,3,5,3,1,4,1,1,7,5,2,0,4,7,9,4,0,9,8,0,5,2,1,4,2,2,7,5,4,2,6
%N A199083 Decimal expansion of x>0 satisfying x^2 + 2*sin(x) = 2.
%C A199083 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199083 G. C. Greubel, <a href="/A199083/b199083.txt">Table of n, a(n) for n = 0..10000</a>
%H A199083 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199083 negative: -1.96188424641083489341928077977489...
%e A199083 positive:  0.774980814423043445958593502470401...
%t A199083 a = 1; b = 2; c = 2;
%t A199083 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199083 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199083 r = x/.FindRoot[f[x] == g[x], {x, -1.97, -1.96}, WorkingPrecision -> 110]
%t A199083 RealDigits[r](* A199082 *)
%t A199083 r = x/.FindRoot[f[x] == g[x], {x, .77, .78}, WorkingPrecision -> 110]
%t A199083 RealDigits[r](* This sequence *)
%o A199083 (PARI) a=1; b=2; c=2; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ _G. C. Greubel_, Feb 20 2019
%o A199083 (Sage) a=1; b=2; c=2; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # _G. C. Greubel_, Feb 20 2019
%Y A199083 Cf. A198866, A199082.
%K A199083 nonn,cons
%O A199083 0,1
%A A199083 _Clark Kimberling_, Nov 02 2011
%E A199083 Terms a(90) onward corrected by _G. C. Greubel_, Feb 20 2019