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%I #9 Oct 10 2014 11:53:42
%S 2,5,8,10,13,16,19,21,24,27,30,32,35,38,41,43,46,49,52,55,57,60,63,66,
%T 68,71,74,77,79,82,85,88,90,93,96,99,101,104,107,110,112,115,118,121,
%U 123,126,129,132,134,137,140,143,145,148,151,154,156,159,162
%N Numbers k such that floor(cot(Pi/(2k+2))) = floor(cot(Pi/(2k))).
%H Clark Kimberling, <a href="/A248520/b248520.txt">Table of n, a(n) for n = 1..10000</a>
%F Conjecture: a(n) ~ Pi/(Pi-2) * n. - _Vaclav Kotesovec_, Oct 09 2014
%e ([cot(Pi/(2k+2))] = [cot(Pi/(2k))]) = (1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0,...), so that A248520 = (2, 5, 8, 10, 13, 16, ...) and A248521 = (1, 3, 4, 6, 7, 9, 11, ...).
%t z = 240; v = Table[Floor[Cot[Pi/(2 n)]], {n, 1, z}];
%t Flatten[Position[Differences[v], 0]] (* A248520 *)
%t Flatten[Position[Differences[v], 1]] (* A248521 *)
%t nmax=200; Select[Range[nmax],Floor[Cot[Pi/(2#+2)]]==Floor[Cot[Pi/(2#)]]&] (* _Vaclav Kotesovec_, Oct 09 2014 *)
%Y Cf. A248521, A033581.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Oct 08 2014
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