%I #10 Aug 22 2018 08:29:33

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

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

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

%N Decimal expansion of least x satisfying x^2 + 6 = 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="/A201572/b201572.txt">Table of n, a(n) for n = 0..10000</a>

%e least: 0.166669163175400949565200320627761299158167...

%e greatest: 3.076894929246192023166693647327725773248...

%t a = 1; c = 6;

%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] (* A201572 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201573 *)

%o (PARI) a=1; c=6; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons

%O 0,2

%A _Clark Kimberling_, Dec 03 2011

%E Terms a(83) onward corrected by _G. C. Greubel_, Aug 21 2018