A223577 - OEIS

%I #28 Jul 17 2021 02:56:54

%S 1,2,3,5,8,10,12,15,17,19,22,24,26,29,31,33,35,38,40,42,45,47,49,52,

%T 54,56,59,61,63,66,68,70,73,75,77,80,82,84,87,89,91,94,96,98,101,103,

%U 105,108,110,112,115,117,119,122,124,126,129,131,133,136,138

%N Positive integers n for which there is exactly one negative integer m such that -n = floor(cot(Pi/(2*m))).

%C Conjecture: A223577(k) = (A223578(k) + k - 1)/2, k=1,2,....

%F a(k) = floor(cot(Pi/(2*A223578(k)))).

%F Conjectures from _Colin Barker_, Jan 03 2014: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n > 6.

%F G.f.: x*(x^17 - x^16 + x^5 + 2*x^4 + x^3 + x^2 + x + 1) / ((x-1)^2*(x^2 + x + 1)). (End)

%t f[n_] := Floor[Cot[Pi/(2 n)]]; Transpose[Select[Tally[Table[-f[-n], {n, 2, 300}]], #[[2]] == 1 &]][[1]] (* _T. D. Noe_, Mar 22 2013 *)

%Y Cf. A024812, A024813, A223578.

%K nonn

%O 1,2

%A _L. Edson Jeffery_, Mar 22 2013