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%I #12 Feb 20 2019 08:11:45
%S 1,4,1,8,3,1,0,0,9,1,6,2,2,5,2,5,0,4,5,6,9,1,9,4,9,6,0,0,8,0,3,7,4,8,
%T 2,3,9,8,7,4,7,3,3,8,7,1,5,0,3,0,4,5,6,6,1,4,3,6,9,8,3,6,8,8,5,4,8,6,
%U 4,1,9,7,7,4,5,6,5,4,9,0,8,3,2,4,4,1,8,4,8,3,8,6,0,2,5,4,1,2,7
%N Decimal expansion of x > 0 satisfying x^2 + sin(x) = 3.
%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A199049/b199049.txt">Table of n, a(n) for n = 1..10000</a>
%e negative: -1.979320146556211460335749713988...
%e positive: 1.4183100916225250456919496008037...
%t a = 1; b = 1; c = 3;
%t f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.98, -1.97}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199048 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199049 *)
%o (PARI) a=1; b=1; c=3; solve(x=0, 1.5, a*x^2 - c + b*sin(x)) \\ _G. C. Greubel_, Feb 19 2019
%o (Sage) a=1; b=1; c=3; (a*x^2 + b*sin(x)==c).find_root(0,2,x) # _G. C. Greubel_, Feb 19 2019
%Y Cf. A198866, A199048.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 02 2011
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