A201664 - OEIS

%I #12 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of least x satisfying 2*x^2 - 1 = 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="/A201664/b201664.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least:  1.039245650797247793231929327242483730000...

%e greatest:  3.086158774377127181225948286358214524...

%t a = 2; c = -1;

%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, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r]     (* A201664 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]

%t RealDigits[r]      (* A201665 *)

%o (PARI) a=2; c=-1; solve(x=1, 2, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 11 2018

%Y Cf. A201564.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Dec 04 2011