cp's OEIS Frontend

A201662 Decimal expansion of greatest x satisfying 10*x^2 = csc(x) and 0 Pi.

%I A201662 #12 Feb 07 2025 16:44:07
%S A201662 3,1,3,1,3,9,4,2,5,3,9,2,0,6,8,9,9,3,5,4,4,4,0,2,8,6,2,2,2,3,8,7,4,7,
%T A201662 0,2,5,1,2,2,6,9,2,6,3,5,3,4,1,8,2,7,3,1,3,6,8,5,9,4,6,4,8,3,8,3,0,4,
%U A201662 0,3,1,1,3,7,1,5,0,1,9,1,2,0
%N A201662 Decimal expansion of greatest x satisfying 10*x^2 = csc(x) and 0 <x< Pi.
%C A201662 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201662 G. C. Greubel, <a href="/A201662/b201662.txt">Table of n, a(n) for n = 1..10000</a>
%H A201662 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201662 least:  0.469931606000588922868653535061891306388300...
%e A201662 greatest:  3.131394253920689935444028622238747025122...
%t A201662 a = 10; c = 0;
%t A201662 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201662 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201662 r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
%t A201662 RealDigits[r]    (* A201660 *)
%t A201662 r = x /.  FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t A201662 RealDigits[r]     (* A201662 *)
%o A201662 (PARI) a=10; c=0; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018
%Y A201662 Cf. A201564.
%K A201662 nonn,cons
%O A201662 1,1
%A A201662 _Clark Kimberling_, Dec 04 2011