cp's OEIS Frontend

A201569 Decimal expansion of greatest x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.

%I A201569 #13 Feb 07 2025 16:44:07
%S A201569 3,0,6,6,9,3,0,1,7,7,6,5,5,7,9,6,7,1,5,9,2,1,0,6,2,7,1,3,7,3,8,1,9,8,
%T A201569 0,7,6,4,5,0,3,0,6,2,1,6,7,1,9,0,4,5,6,7,5,9,0,8,5,3,0,1,7,8,9,3,4,9,
%U A201569 7,7,9,4,1,5,5,5,0,6,8,7,0,1,3,2,5,0,4,0,0,1,4,8,0,6,4,8,0,3,1
%N A201569 Decimal expansion of greatest x satisfying x^2 + 4 = csc(x) and 0 < x < Pi.
%C A201569 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201569 G. C. Greubel, <a href="/A201569/b201569.txt">Table of n, a(n) for n = 1..10000</a>
%H A201569 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201569 least:  0.2487490007162959853652924083716941039...
%e A201569 greatest:  3.0669301776557967159210627137381980...
%t A201569 a = 1; c = 4;
%t A201569 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201569 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201569 r = x /. FindRoot[f[x] == g[x], {x, .2, .3}, WorkingPrecision -> 110]
%t A201569 RealDigits[r]   (* A201568 *)
%t A201569 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201569 RealDigits[r]   (* A201569 *)
%o A201569 (PARI) a=1; c=4; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201569 Cf. A201564.
%K A201569 nonn,cons
%O A201569 1,1
%A A201569 _Clark Kimberling_, Dec 03 2011