cp's OEIS Frontend

A201571 Decimal expansion of greatest x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

%I A201571 #13 Feb 07 2025 16:44:07
%S A201571 3,0,7,2,2,7,9,8,3,0,0,5,1,2,5,0,3,3,5,8,5,9,8,6,6,4,6,0,4,6,4,6,9,9,
%T A201571 0,6,0,3,6,3,7,2,9,1,3,7,8,0,4,8,4,8,3,4,3,3,0,6,3,1,4,0,6,9,7,8,4,5,
%U A201571 2,0,7,7,8,5,0,3,1,7,1,7,0,5,5,2,3,2,0,3,8,1,8,3,5,8,4,0,9,6,1
%N A201571 Decimal expansion of greatest x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.
%C A201571 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201571 G. C. Greubel, <a href="/A201571/b201571.txt">Table of n, a(n) for n = 1..10000</a>
%H A201571 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201571 least:  0.19974229281947213708674051595534811453...
%e A201571 greatest:  3.07227983005125033585986646046469906...
%t A201571 a = 1; c = 5;
%t A201571 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201571 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201571 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201571 RealDigits[r]   (* A201570 *)
%t A201571 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201571 RealDigits[r]   (* A201571 *)
%o A201571 (PARI) a=1; c=5; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201571 Cf. A201564.
%K A201571 nonn,cons
%O A201571 1,1
%A A201571 _Clark Kimberling_, Dec 03 2011