cp's OEIS Frontend

A201575 Decimal expansion of greatest x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.

%I A201575 #12 Jan 30 2025 13:53:01
%S A201575 3,0,8,0,9,2,0,2,3,2,2,9,5,2,0,6,8,0,4,5,5,9,3,5,8,4,9,8,2,1,2,7,5,3,
%T A201575 7,0,1,0,8,7,2,6,9,9,6,9,0,8,2,4,2,1,1,8,5,7,5,7,2,2,8,1,7,4,8,5,3,8,
%U A201575 9,4,3,8,2,4,7,7,5,0,5,0,9,0,3,9,8,7,9,1,5,9,7,4,0,2,6,4,8,9,4
%N A201575 Decimal expansion of greatest x satisfying x^2 + 7 = csc(x) and 0 < x < Pi.
%C A201575 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201575 G. C. Greubel, <a href="/A201575/b201575.txt">Table of n, a(n) for n = 1..10000</a>
%H A201575 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201575 least:  0.14292758299392086700431044307554748240884...
%e A201575 greatest:  3.08092023229520680455935849821275370108...
%t A201575 a = 1; c = 7;
%t A201575 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201575 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201575 r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
%t A201575 RealDigits[r]   (* A201574 *)
%t A201575 r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]
%t A201575 RealDigits[r]   (* A201575 *)
%o A201575 (PARI) a=1; c=7; solve(x=3, 3.1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018
%Y A201575 Cf. A201564.
%K A201575 nonn,cons
%O A201575 1,1
%A A201575 _Clark Kimberling_, Dec 03 2011