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%I #9 Sep 12 2018 01:33:47
%S 3,1,0,5,7,9,1,2,2,9,3,6,3,0,8,2,2,7,7,9,2,8,9,6,7,9,3,1,6,1,4,3,1,4,
%T 3,0,3,5,9,5,3,6,9,7,6,5,5,5,2,9,1,7,0,3,3,2,2,8,1,2,7,8,5,1,1,4,2,9,
%U 5,2,0,6,7,4,2,4,0,0,2,7,5,4,0,8,2,0,1,2,1,2,0,0,3,9,9,4,5,3,6
%N Decimal expansion of greatest x satisfying 3*x^2 - 1 = csc(x) and 0<x<Pi.
%C See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A201667/b201667.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 0.875943738724356441549462867955303876323370...
%e greatest: 3.105791229363082277928967931614314303595...
%t a = 3; c = -1;
%t f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201666 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201667 *)
%o (PARI) a=3; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018
%Y Cf. A201564.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 04 2011
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