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A248521 Numbers k such that floor(cot(Pi/(2k+2))) = floor(cot(Pi/(2k))) + 1. 2

%I #8 Oct 10 2014 11:53:17

%S 1,3,4,6,7,9,11,12,14,15,17,18,20,22,23,25,26,28,29,31,33,34,36,37,39,

%T 40,42,44,45,47,48,50,51,53,54,56,58,59,61,62,64,65,67,69,70,72,73,75,

%U 76,78,80,81,83,84,86,87,89,91,92,94,95,97,98,100,102

%N Numbers k such that floor(cot(Pi/(2k+2))) = floor(cot(Pi/(2k))) + 1.

%H Clark Kimberling, <a href="/A248521/b248521.txt">Table of n, a(n) for n = 1..10000</a>

%F Conjecture: a(n) ~ Pi*n/2. - _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=100; Select[Range[nmax],Floor[Cot[Pi/(2#+2)]]==Floor[Cot[Pi/(2#)]]+1&] (* _Vaclav Kotesovec_, Oct 09 2014 *)

%Y Cf. A248520, A033581.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Oct 08 2014

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