cp's OEIS Frontend

A201579 Decimal expansion of least x satisfying x^2 + 9 = csc(x) and 0 < x < Pi.

%I A201579 #14 Feb 07 2025 16:44:07
%S A201579 1,1,1,1,8,7,6,4,9,5,3,0,3,3,6,5,5,2,4,1,1,3,2,1,6,9,1,8,0,0,6,5,7,5,
%T A201579 3,3,6,1,1,7,8,7,3,4,2,3,4,6,0,7,0,0,3,7,0,8,5,6,9,6,1,2,1,2,7,2,8,3,
%U A201579 8,6,1,8,4,4,7,2,8,6,5,9,0,9,2,5,8,1,7,6,4,2,8,9,2,7,5,3,2,4,7
%N A201579 Decimal expansion of least x satisfying x^2 + 9 = csc(x) and 0 < x < Pi.
%C A201579 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201579 G. C. Greubel, <a href="/A201579/b201579.txt">Table of n, a(n) for n = 0..10000</a>
%H A201579 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201579 least:  0.111187649530336552411321691800657533611...
%e A201579 greatest:  3.087609602783606133001190498846701507...
%t A201579 a = 1; c = 9;
%t A201579 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201579 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201579 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201579 RealDigits[r]   (* A201579 *)
%t A201579 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201579 RealDigits[r]   (* A201580 *)
%o A201579 (PARI) a=1; c=9; solve(x=0.1, .2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201579 Cf. A201564.
%K A201579 nonn,cons
%O A201579 0,5
%A A201579 _Clark Kimberling_, Dec 03 2011