cp's OEIS Frontend

A201570 Decimal expansion of least x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.

%I A201570 #13 Feb 07 2025 16:44:07
%S A201570 1,9,9,7,4,2,2,9,2,8,1,9,4,7,2,1,3,7,0,8,6,7,4,0,5,1,5,9,5,5,3,4,8,1,
%T A201570 1,4,5,3,2,5,4,5,4,4,3,9,0,3,2,5,3,2,4,3,3,4,5,3,8,3,3,5,7,7,9,2,2,9,
%U A201570 6,3,1,0,3,9,3,7,2,6,7,6,1,4,9,0,4,3,4,8,2,7,7,7,7,7,5,6,0,7,1
%N A201570 Decimal expansion of least x satisfying x^2 + 5 = csc(x) and 0 < x < Pi.
%C A201570 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201570 G. C. Greubel, <a href="/A201570/b201570.txt">Table of n, a(n) for n = 0..10000</a>
%H A201570 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201570 least:  0.19974229281947213708674051595534811453...
%e A201570 greatest:  3.07227983005125033585986646046469906...
%t A201570 a = 1; c = 5;
%t A201570 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201570 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201570 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201570 RealDigits[r]   (* A201570 *)
%t A201570 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201570 RealDigits[r]   (* A201571 *)
%o A201570 (PARI) a=1; c=5; solve(x=0.1, 0.2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201570 Cf. A201564.
%K A201570 nonn,cons
%O A201570 0,2
%A A201570 _Clark Kimberling_, Dec 03 2011