A201738 - OEIS

%I #9 Sep 13 2018 02:55:37

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

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

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

%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.

%C There is a greatest number c for which x^2-c=csc(x) for some number x satisfying 0<x<pi.  The number c is between 4 and 5.

%H G. C. Greubel, <a href="/A201738/b201738.txt">Table of n, a(n) for n = 1..10000</a>

%e least:  2.31504693361737481767157626271919435080...

%e greatest:  2.91834369901820138765983699207605876...

%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, 2.4}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201737 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201738 *)

%o (PARI) a=1; c=-4; solve(x=2.5, 3, 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