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%I #10 Aug 22 2018 08:29:54
%S 3,0,6,6,9,3,0,1,7,7,6,5,5,7,9,6,7,1,5,9,2,1,0,6,2,7,1,3,7,3,8,1,9,8,
%T 0,7,6,4,5,0,3,0,6,2,1,6,7,1,9,0,4,5,6,7,5,9,0,8,5,3,0,1,7,8,9,3,4,9,
%U 7,7,9,4,1,5,5,5,0,6,8,7,0,1,3,2,5,0,4,0,0,1,4,8,0,6,4,8,0,3,1
%N Decimal expansion of greatest x satisfying x^2 + 4 = 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="/A201569/b201569.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 0.2487490007162959853652924083716941039...
%e greatest: 3.0669301776557967159210627137381980...
%t a = 1; c = 4;
%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, .2, .3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201568 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201569 *)
%o (PARI) a=1; c=4; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y Cf. A201564.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 03 2011
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