%I #10 Aug 23 2018 02:15:14
%S 6,4,4,8,9,7,4,7,5,5,4,3,6,7,3,8,3,4,4,4,3,3,5,7,3,9,0,0,4,4,4,7,4,5,
%T 2,0,1,7,0,1,3,6,8,0,5,7,9,8,7,6,3,3,7,5,0,8,8,3,4,1,4,4,8,8,6,5,5,0,
%U 7,5,9,7,3,0,8,2,2,8,5,9,1,9,6,9,6,3,7,0,0,3,0,4,9,4,5,1,7,5,1
%N Decimal expansion of least x satisfying 4*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="/A201587/b201587.txt">Table of n, a(n) for n = 0..10000</a>
%e least: 0.6448974755436738344433573900444745201701368...
%e greatest: 3.1158390512762535211310850151952082587811...
%t a = 4; 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, .6, .7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201587 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201588 *)
%o (PARI) a=4; c=0; solve(x=0.6, 0.7, 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