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%I #9 Sep 13 2018 02:56:49
%S 3,1,2,6,7,6,3,3,5,4,8,1,7,8,4,3,9,5,8,3,2,4,7,1,0,5,4,3,0,4,1,3,9,3,
%T 5,0,0,8,6,9,5,6,0,6,7,8,0,4,2,4,0,6,1,3,9,9,3,3,0,3,2,1,0,4,5,3,3,0,
%U 3,9,5,9,0,7,3,7,1,4,3,9,0,9,5,1,1,5,5,1,5,2,7,8,9,8,4,2,3,6,0
%N Decimal expansion of greatest x satisfying 7*x^2 - 1 = 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="/A201675/b201675.txt">Table of n, a(n) for n = 1..10000</a>
%e least: 0.62272709431369510379503993928652289013...
%e greatest: 3.12676335481784395832471054304139350...
%t a = 7; c = -1;
%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] (* A201674 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201675 *)
%o (PARI) a=7; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y Cf. A201564.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Dec 04 2011
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