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%I #6 Oct 09 2014 09:48:15
%S 0,1,2,3,4,5,7,9,11,13,15,18,21,24,27,30,34,38,42,46,50,55,60,65,70,
%T 75,80,86,92,98,104,111,118,125,132,139,146,154,162,170,178,186,195,
%U 204,213,222,231,241,251,261,271,281,292,303,313,325,336,347,359
%N Floor( 1/(n*tan(Pi/n) - Pi) ).
%C This sequence provedes insight into the manner of convergence of n*tan(Pi/n) to Pi.
%H Clark Kimberling, <a href="/A248421/b248421.txt">Table of n, a(n) for n = 3..2000</a>
%F a(n) ~ 3*n^2/Pi^3. - _Vaclav Kotesovec_, Oct 09 2014
%e n ... n*tan(Pi/n)-Pi) ... 1/(n*tan(Pi/n)-Pi)
%e 3 ... 2.05456 ........... 0.486722
%e 4 ... 0.85840 ........... 1.16495
%e 5 ... 0.49112 ........... 2.03616
%e 6 ... 0.32250 ........... 3.10069
%t z = 550; p[k_] := p[k] = k*Tan[Pi/k]; N[Table[p[n] - Pi, {n, 3, z/10}]]
%t f[n_] := f[n] = Select[2 + Range[z], p[#] - Pi < 1/n &, 1];
%t u = Flatten[Table[f[n], {n, 3, z}]] (* A248418 *)
%t g = Table[Floor[1/(p[n] - Pi)], {n, 3, z}] (* A248421 *)
%Y Cf. A248418, A248419, A248420.
%K nonn,easy
%O 3,3
%A _Clark Kimberling_, Oct 07 2014
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