%I
%S 3,1,2,1,0,5,9,4,6,3,5,2,3,8,2,7,4,1,5,3,6,0,1,7,5,7,0,0,0,3,4,0,9,2,
%T 0,4,8,9,1,0,7,4,9,9,6,8,4,4,7,8,4,7,8,2,7,1,2,2,2,5,2,7,1,0,2,4,0,7,
%U 1,2,3,5,0,6,2,6,9,9,8,4,0,2,3,6,0,2,1,6,0,4,6,0,7,0,9,2,7,5,4,3
%N Decimal expansion of greatest x satisfying 5*x^2 = 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="/A201590/b201590.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 0.596626819860704546761832859082141048303653100...
%e greatest: 3.121059463523827415360175700034092048910749...
%t a = 5; c = 0;
%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, .5, .6}, WorkingPrecision > 110]
%t RealDigits[r] (* A201589 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision > 110]
%t RealDigits[r] (* A201590 *)
%o (PARI) a=5; c=0; solve(x=3.1, 3.14, a*x^2 + c  1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y Cf. A201564.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 03 2011
%E Terms a(88) onward corrected by _G. C. Greubel_, Aug 22 2018
