A248520 Numbers k such that floor(cot(Pi/(2k+2))) = floor(cot(Pi/(2k))).

2, 5, 8, 10, 13, 16, 19, 21, 24, 27, 30, 32, 35, 38, 41, 43, 46, 49, 52, 55, 57, 60, 63, 66, 68, 71, 74, 77, 79, 82, 85, 88, 90, 93, 96, 99, 101, 104, 107, 110, 112, 115, 118, 121, 123, 126, 129, 132, 134, 137, 140, 143, 145, 148, 151, 154, 156, 159, 162

Offset

1,1

Links

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

Formula

Conjecture: a(n) ~ Pi/(Pi-2) * n. - 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=200; Select[Range[nmax], Floor[Cot[Pi/(2#+2)]]==Floor[Cot[Pi/(2#)]]&] (* Vaclav Kotesovec, Oct 09 2014 *)

Crossrefs

Cf. A248521, A033581.

Sequence in context: A054088 A186540 A059556 * A247780 A189365 A024509

Adjacent sequences: A248517 A248518 A248519 * A248521 A248522 A248523

Keyword

nonn,easy

Author

Clark Kimberling, Oct 08 2014

Status

approved