A248421 Floor( 1/(n*tan(Pi/n) - Pi) ).

0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 80, 86, 92, 98, 104, 111, 118, 125, 132, 139, 146, 154, 162, 170, 178, 186, 195, 204, 213, 222, 231, 241, 251, 261, 271, 281, 292, 303, 313, 325, 336, 347, 359

Offset

3,3

Comments

This sequence provedes insight into the manner of convergence of n*tan(Pi/n) to Pi.

Links

Clark Kimberling, Table of n, a(n) for n = 3..2000

Formula

a(n) ~ 3*n^2/Pi^3. - Vaclav Kotesovec, Oct 09 2014

Example

n ... n*tan(Pi/n)-Pi) ... 1/(n*tan(Pi/n)-Pi)
3 ... 2.05456 ........... 0.486722
4 ... 0.85840 ........... 1.16495
5 ... 0.49112 ........... 2.03616
6 ... 0.32250 ........... 3.10069

Mathematica

z = 550; p[k_] := p[k] = k*Tan[Pi/k]; N[Table[p[n] - Pi, {n, 3, z/10}]]
f[n_] := f[n] = Select[2 + Range[z], p[#] - Pi < 1/n &, 1];
u = Flatten[Table[f[n], {n, 3, z}]]  (* A248418 *)
g = Table[Floor[1/(p[n] - Pi)], {n, 3, z}]  (* A248421 *)

Crossrefs

Cf. A248418, A248419, A248420.

Sequence in context: A325461 A135785 A262249 * A008732 A130520 A005706

Adjacent sequences: A248418 A248419 A248420 * A248422 A248423 A248424

Keyword

nonn,easy

Author

Clark Kimberling, Oct 07 2014

Status

approved