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%I #10 Aug 23 2018 02:14:59
%S 5,9,6,6,2,6,8,1,9,8,6,0,7,0,4,5,4,6,7,6,1,8,3,2,8,5,9,0,8,2,1,4,1,0,
%T 4,8,3,0,3,6,5,3,1,0,0,8,7,0,2,9,3,0,5,7,4,4,7,1,8,2,0,4,7,7,5,8,3,7,
%U 4,7,8,6,0,6,4,1,9,9,1,6,3,4,1,9,4,0,7,6,9,5,4,7,5,8,8,9,5,2,2,7,8
%N Decimal expansion of least 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="/A201589/b201589.txt">Table of n, a(n) for n = 0..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=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y Cf. A201564.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 03 2011
%E Terms a(90) onward corrected by _G. C. Greubel_, Aug 22 2018
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