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%I #12 Feb 20 2019 16:02:10
%S 4,2,3,0,2,8,1,8,1,8,8,5,1,6,0,4,2,8,8,5,1,2,9,3,3,2,4,7,3,2,6,0,7,1,
%T 8,9,5,7,2,6,9,9,8,1,0,8,4,9,1,9,9,6,0,1,7,7,7,0,2,2,5,5,3,1,6,0,9,3,
%U 4,1,1,9,8,1,1,0,6,1,3,3,0,2,6,6,3,3,0,5,4,9,3,8,0,7,7,9,9,7,2,1,8
%N Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.
%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A199081/b199081.txt">Table of n, a(n) for n = 0..10000</a>
%e negative: -1.7251712054289301271344240020632...
%e positive: 0.42302818188516042885129332473260...
%t a = 1; b = 2; c = 1;
%t f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199080 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199081 *)
%o (PARI) a=1; b=2; c=1; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ _G. C. Greubel_, Feb 20 2019
%o (Sage) a=1; b=2; c=1; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # _G. C. Greubel_, Feb 20 2019
%Y Cf. A198866, A199080.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 02 2011
%E Terms a(83) onward corrected by _G. C. Greubel_, Feb 20 2019
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