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A248360 a(n) = floor( 1/(1 - cos(Pi/n)) ).

%I A248360 #16 Nov 11 2024 21:20:15
%S A248360 0,1,2,3,5,7,10,13,16,20,24,29,34,39,45,52,58,65,73,81,89,98,107,116,
%T A248360 126,137,147,159,170,182,194,207,220,234,248,262,277,292,308,324,340,
%U A248360 357,374,392,410,428,447,467,486,506,527,548,569,591,613,635,658
%N A248360 a(n) = floor( 1/(1 - cos(Pi/n)) ).
%C A248360 This sequence provides insight into the manner of convergence of the sequence cos(Pi/n).
%H A248360 Clark Kimberling, <a href="/A248360/b248360.txt">Table of n, a(n) for n = 1..1000</a>
%F A248360 a(n) ~ 2*n^2/Pi^2. - _Vaclav Kotesovec_, Oct 09 2014
%e A248360 Approximations:
%e A248360 n ... 1-cos(Pi/n) ... 1/(1-cos(Pi/n))
%e A248360 1 ... 2 ............. 0.5
%e A248360 2 ... 1 ............. 1
%e A248360 3 ... 0.5 ........... 2
%e A248360 4 ... 0.292893 ...... 3.31421
%e A248360 5 ... 0.190983 ...... 5.23607
%e A248360 6 ... 0.133975 ...... 7.4741
%t A248360 z = 800; f[n_] := f[n] = Select[Range[z], Cos[Pi/#] + 1/(#*n) > 1 &, 1];
%t A248360 u = Flatten[Table[f[n], {n, 1, z}]]  (* A248359 *)
%t A248360 Table[Floor[1/(1 - Cos[Pi/n])], {n, 1, z/10}]  (* A248360 *)
%Y A248360 Cf. A248360.
%K A248360 nonn,easy
%O A248360 1,3
%A A248360 _Clark Kimberling_, Oct 07 2014