cp's OEIS Frontend

A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.

%I A201567 #13 Feb 07 2025 16:44:07
%S A201567 3,0,6,0,6,4,7,6,2,1,6,7,4,3,9,0,6,4,9,4,6,7,0,2,1,0,6,1,4,4,1,5,7,5,
%T A201567 3,7,2,7,8,8,8,9,0,1,2,3,3,7,6,9,2,2,2,7,4,3,9,7,9,9,5,2,3,0,0,1,8,8,
%U A201567 1,8,3,7,3,7,3,6,9,0,6,0,9,4,1,8,6,6,2,9,2,4,4,0,1,7,3,8,0,7,6
%N A201567 Decimal expansion of greatest x satisfying x^2 + 3 = csc(x) and 0 < x < Pi.
%C A201567 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201567 G. C. Greubel, <a href="/A201567/b201567.txt">Table of n, a(n) for n = 1..10000</a>
%H A201567 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201567 least:  0.3276482471136686780982477062098195298...
%e A201567 greatest:  3.0606476216743906494670210614415753...
%t A201567 a = 1; c = 3;
%t A201567 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201567 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201567 r = x /. FindRoot[f[x] == g[x], {x, .3, .4}, WorkingPrecision -> 110]
%t A201567 RealDigits[r]    (* A201567 *)
%t A201567 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201567 RealDigits[r]   (* A201568 *)
%o A201567 (PARI) a=1; c=3; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201567 Cf. A201564.
%K A201567 nonn,cons
%O A201567 1,1
%A A201567 _Clark Kimberling_, Dec 03 2011