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%I #10 Aug 22 2018 08:28:20
%S 3,0,9,0,4,2,1,2,7,0,1,5,2,1,5,1,4,5,3,6,5,1,4,9,7,4,4,3,8,9,9,9,2,0,
%T 5,3,4,3,8,7,8,8,2,1,3,8,3,1,5,6,3,5,0,1,4,0,8,5,5,5,5,1,8,9,9,6,6,3,
%U 6,3,1,5,9,8,0,6,4,7,6,1,2,8,4,0,6,0,6,1,1,0,6,8,9,9,4,4,5,3,4
%N Decimal expansion of greatest x satisfying x^2 + 10 = 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="/A201581/b201581.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 0.100066884072919309279805384459381115060...
%e greatest: 3.090421270152151453651497443899920534...
%t a = 1; c = 10;
%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, .1, .2}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201578 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201581 *)
%o (PARI) a=1; c=10; 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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