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A201590 Decimal expansion of greatest x satisfying 5*x^2 = csc(x) and 0 < x < Pi. 3

%I

%S 3,1,2,1,0,5,9,4,6,3,5,2,3,8,2,7,4,1,5,3,6,0,1,7,5,7,0,0,0,3,4,0,9,2,

%T 0,4,8,9,1,0,7,4,9,9,6,8,4,4,7,8,4,7,8,2,7,1,2,2,2,5,2,7,1,0,2,4,0,7,

%U 1,2,3,5,0,6,2,6,9,9,8,4,0,2,3,6,0,2,1,6,0,4,6,0,7,0,9,2,7,5,4,3

%N Decimal expansion of greatest 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="/A201590/b201590.txt">Table of n, a(n) for n = 1..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=3.1, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Dec 03 2011

%E Terms a(88) onward corrected by _G. C. Greubel_, Aug 22 2018

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Last modified February 24 03:22 EST 2020. Contains 332195 sequences. (Running on oeis4.)