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%I #11 Sep 12 2018 01:34:26
%S 6,6,1,7,3,6,5,5,7,1,6,9,7,4,4,2,2,6,2,4,1,8,2,9,8,3,7,0,9,4,0,0,2,6,
%T 0,7,7,4,7,4,7,9,8,8,1,3,8,2,5,3,8,4,1,0,2,5,2,2,4,5,7,7,6,0,7,8,5,2,
%U 8,6,9,1,9,6,5,1,3,1,9,6,9,6,0,3,3,1,1,1,0,9,3,6,1,5,6,2,0,0,2
%N Decimal expansion of least x satisfying 6*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="/A201672/b201672.txt">Table of n, a(n) for n = 0..10000</a>
%e least: 0.66173655716974422624182983709400260774...
%e greatest: 3.12421996270608159489890621092028546...
%t a = 6; 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, .6, .7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201672 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201673 *)
%o (PARI) a=6; c=-1; solve(x=.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018
%Y Cf. A201564.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 04 2011
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