%I #13 Feb 07 2025 16:44:07
%S 5,3,1,0,9,3,7,8,3,2,2,8,7,7,5,5,6,9,5,4,2,4,5,4,2,6,2,8,7,2,7,2,8,7,
%T 8,8,1,2,7,0,9,7,3,8,1,6,4,0,0,6,1,0,9,0,6,3,7,8,1,0,4,1,5,3,4,8,0,6,
%U 2,2,0,8,4,6,0,4,4,8,5,0,5,1,0,5,1,5,6,1,0,9,2,0,6,1,2,7,1,3,4
%N Decimal expansion of least x satisfying 7*x^2 = csc(x) and 0 < x < Pi.
%C See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A201654/b201654.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e least: 0.53109378322877556954245426287272878812709738...
%e greatest: 3.12698210171419101601393999273016371798979...
%t a = 7; c = 0;
%t f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201654 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201655 *)
%o (PARI) a=7; c=0; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y Cf. A201564.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 04 2011