cp's OEIS Frontend

A201587 Decimal expansion of least x satisfying 4*x^2 = csc(x) and 0 < x < Pi.

%I A201587 #13 Feb 07 2025 16:44:07
%S A201587 6,4,4,8,9,7,4,7,5,5,4,3,6,7,3,8,3,4,4,4,3,3,5,7,3,9,0,0,4,4,4,7,4,5,
%T A201587 2,0,1,7,0,1,3,6,8,0,5,7,9,8,7,6,3,3,7,5,0,8,8,3,4,1,4,4,8,8,6,5,5,0,
%U A201587 7,5,9,7,3,0,8,2,2,8,5,9,1,9,6,9,6,3,7,0,0,3,0,4,9,4,5,1,7,5,1
%N A201587 Decimal expansion of least x satisfying 4*x^2 = csc(x) and 0 < x < Pi.
%C A201587 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201587 G. C. Greubel, <a href="/A201587/b201587.txt">Table of n, a(n) for n = 0..10000</a>
%H A201587 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201587 least:  0.6448974755436738344433573900444745201701368...
%e A201587 greatest:  3.1158390512762535211310850151952082587811...
%t A201587 a = 4; c = 0;
%t A201587 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201587 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201587 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201587 RealDigits[r]   (* A201587 *)
%t A201587 r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t A201587 RealDigits[r]   (* A201588 *)
%o A201587 (PARI) a=4; c=0; solve(x=0.6, 0.7, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y A201587 Cf. A201564.
%K A201587 nonn,cons
%O A201587 0,1
%A A201587 _Clark Kimberling_, Dec 03 2011