cp's OEIS Frontend

A201655 Decimal expansion of greatest x satisfying 7*x^2 = csc(x) and 0 < x < Pi.

%I A201655 #13 Feb 07 2025 16:44:07
%S A201655 3,1,2,6,9,8,2,1,0,1,7,1,4,1,9,1,0,1,6,0,1,3,9,3,9,9,9,2,7,3,0,1,6,3,
%T A201655 7,1,7,9,8,9,7,9,7,5,8,0,5,9,7,5,5,5,6,2,5,6,1,1,3,4,3,6,3,8,0,1,0,7,
%U A201655 5,2,7,1,7,5,3,0,4,3,9,4,9,2,1,5,2,4,6,1,1,6,8,1,9,2,6,7,8,6,7
%N A201655 Decimal expansion of greatest x satisfying 7*x^2 = csc(x) and 0 < x < Pi.
%C A201655 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201655 G. C. Greubel, <a href="/A201655/b201655.txt">Table of n, a(n) for n = 1..10000</a>
%H A201655 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201655 least:  0.53109378322877556954245426287272878812709738...
%e A201655 greatest:  3.12698210171419101601393999273016371798979...
%t A201655 a = 7; c = 0;
%t A201655 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201655 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201655 r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t A201655 RealDigits[r]   (* A201654 *)
%t A201655 r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t A201655 RealDigits[r]   (* A201655 *)
%o A201655 (PARI) a=7; c=0; solve(x=3.1, 3.14, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y A201655 Cf. A201564.
%K A201655 nonn,cons
%O A201655 1,1
%A A201655 _Clark Kimberling_, Dec 04 2011