cp's OEIS Frontend

A201738 Decimal expansion of greatest x satisfying x^2 - 4 = csc(x) and 0

%I A201738 #12 Feb 07 2025 16:44:07
%S A201738 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 A201738 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 A201738 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 A201738 Decimal expansion of greatest x satisfying x^2 - 4 = csc(x) and 0<x<Pi.
%C A201738 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%C A201738 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 A201738 G. C. Greubel, <a href="/A201738/b201738.txt">Table of n, a(n) for n = 1..10000</a>
%H A201738 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201738 least:  2.31504693361737481767157626271919435080...
%e A201738 greatest:  2.91834369901820138765983699207605876...
%t A201738 a = 1; c = -4;
%t A201738 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201738 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201738 r = x /. FindRoot[f[x] == g[x], {x, 2.3, 2.4}, WorkingPrecision -> 110]
%t A201738 RealDigits[r]   (* A201737 *)
%t A201738 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201738 RealDigits[r]   (* A201738 *)
%o A201738 (PARI) a=1; c=-4; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y A201738 Cf. A201564.
%K A201738 nonn,cons
%O A201738 1,1
%A A201738 _Clark Kimberling_, Dec 04 2011