A223578 Positive integers n for which f(-n-1) < f(-n) < f(-n+1), where f(m) = floor(cot(Pi/(2m))).

2, 3, 4, 7, 12, 15, 18, 23, 26, 29, 34, 37, 40, 45, 48, 51, 54, 59, 62, 65, 70, 73, 76, 81, 84, 87, 92, 95, 98, 103, 106, 109, 114, 117, 120, 125, 128, 131, 136, 139, 142, 147, 150, 153, 158, 161, 164, 169, 172, 175, 180, 183, 186, 191, 194, 197

Offset

1,1

Comments

Conjecture: A223568(k) = 2*A223577(k)-k+1, k=1,2,....

Links

Table of n, a(n) for n=1..56.

Formula

Conjecture: a(n) = a(n-1)+a(n-3)-a(n-4) for n>6. G.f.: x*(2*x^17-2*x^16+2*x^5+4*x^4+x^3+x^2+x+2) / ((x-1)^2*(x^2+x+1)). - Colin Barker, Jan 03 2014

Mathematica

f[n_] := Floor[Cot[Pi/(2 n)]]; Select[Range[2, 200],  f[-# - 1] < f[-#] < f[-# + 1] &] (* T. D. Noe, Mar 22 2013 *)

Crossrefs

Cf. A024812, A024813, A223577.

Sequence in context: A372266 A116628 A140463 * A073147 A249578 A325244

Adjacent sequences: A223575 A223576 A223577 * A223579 A223580 A223581

Keyword

nonn

Author

L. Edson Jeffery, Mar 22 2013

Status

approved