A201566 - OEIS

%I #13 Feb 07 2025 16:44:07

%S 3,2,7,6,4,8,2,4,7,1,1,3,6,6,8,6,7,8,0,9,8,2,4,7,7,0,6,2,0,9,8,1,9,5,

%T 2,9,8,4,4,3,7,8,4,5,2,8,2,0,0,2,4,4,8,6,4,8,9,9,2,1,7,0,7,4,8,2,1,6,

%U 1,7,1,2,6,7,5,1,4,2,8,3,5,6,9,6,9,5,8,9,9,8,1,6,1,6,1,7,2,1,8

%N Decimal expansion of least x satisfying x^2 + 3 = 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="/A201566/b201566.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:  0.3276482471136686780982477062098195298...

%e greatest:  3.0606476216743906494670210614415753...

%t a = 1; c = 3;

%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, .3, .4}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201567 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.1}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201568 *)

%o (PARI) a=1; c=3; solve(x=0.2, 0.5, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 21 2018

%Y Cf. A201564.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Dec 03 2011