A201656 - OEIS

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

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

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

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

%N Decimal expansion of least x satisfying 8*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="/A201656/b201656.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:  0.507262199349103778265812147726404197638586...

%e greatest:  3.128823571901654937275752484725028832935...

%t a = 8; 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]   (* A201656 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.14}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A201657 *)

%o (PARI) a=8; 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