cp's OEIS Frontend

A201672 Decimal expansion of least x satisfying 6*x^2 - 1 = csc(x) and 0

%I A201672 #14 Feb 07 2025 16:44:07
%S A201672 6,6,1,7,3,6,5,5,7,1,6,9,7,4,4,2,2,6,2,4,1,8,2,9,8,3,7,0,9,4,0,0,2,6,
%T A201672 0,7,7,4,7,4,7,9,8,8,1,3,8,2,5,3,8,4,1,0,2,5,2,2,4,5,7,7,6,0,7,8,5,2,
%U A201672 8,6,9,1,9,6,5,1,3,1,9,6,9,6,0,3,3,1,1,1,0,9,3,6,1,5,6,2,0,0,2
%N A201672 Decimal expansion of least x satisfying 6*x^2 - 1 = csc(x) and 0<x<Pi.
%C A201672 See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H A201672 G. C. Greubel, <a href="/A201672/b201672.txt">Table of n, a(n) for n = 0..10000</a>
%H A201672 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201672 least:  0.66173655716974422624182983709400260774...
%e A201672 greatest:  3.12421996270608159489890621092028546...
%t A201672 a = 6; c = -1;
%t A201672 f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t A201672 Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t A201672 r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t A201672 RealDigits[r]     (* A201672 *)
%t A201672 r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]
%t A201672 RealDigits[r]     (* A201673 *)
%o A201672 (PARI) a=6; c=-1; solve(x=.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018
%Y A201672 Cf. A201564.
%K A201672 nonn,cons
%O A201672 0,1
%A A201672 _Clark Kimberling_, Dec 04 2011