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

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, 40, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 76, 78, 80, 81, 83, 84, 86, 87, 89, 91, 92, 94, 95, 97, 98, 100, 102

Offset

1,2

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

Conjecture: a(n) ~ Pi*n/2. - Vaclav Kotesovec, Oct 09 2014

Example

([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, ...).

Mathematica

z = 240; v = Table[Floor[Cot[Pi/(2 n)]], {n, 1, z}];
Flatten[Position[Differences[v], 0]] (* A248520 *)
Flatten[Position[Differences[v], 1]] (* A248521 *)
nmax=100; Select[Range[nmax], Floor[Cot[Pi/(2#+2)]]==Floor[Cot[Pi/(2#)]]+1&] (* Vaclav Kotesovec, Oct 09 2014 *)

Crossrefs

Cf. A248520, A033581.

Sequence in context: A018825 A247779 A243989 * A059555 A186539 A054385

Adjacent sequences: A248518 A248519 A248520 * A248522 A248523 A248524

Keyword

nonn,easy

Author

Clark Kimberling, Oct 08 2014

Status

approved