A223577 Positive integers n for which there is exactly one negative integer m such that -n = floor(cot(Pi/(2*m))).

1, 2, 3, 5, 8, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 70, 73, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 98, 101, 103, 105, 108, 110, 112, 115, 117, 119, 122, 124, 126, 129, 131, 133, 136, 138

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..61.

Formula

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

Conjectures from Colin Barker, Jan 03 2014: (Start)

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

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)

Mathematica

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 *)

Crossrefs

Cf. A024812, A024813, A223578.

Sequence in context: A369064 A277625 A098177 * A256793 A193640 A112045

Adjacent sequences: A223574 A223575 A223576 * A223578 A223579 A223580

Keyword

nonn

Author

L. Edson Jeffery, Mar 22 2013

Status

approved