A248360 a(n) = floor( 1/(1 - cos(Pi/n)) ).

0, 1, 2, 3, 5, 7, 10, 13, 16, 20, 24, 29, 34, 39, 45, 52, 58, 65, 73, 81, 89, 98, 107, 116, 126, 137, 147, 159, 170, 182, 194, 207, 220, 234, 248, 262, 277, 292, 308, 324, 340, 357, 374, 392, 410, 428, 447, 467, 486, 506, 527, 548, 569, 591, 613, 635, 658

Offset: 1

Author

Clark Kimberling, Oct 07 2014

Keywords

• nonn
• easy

Comments

This sequence provides insight into the manner of convergence of the sequence cos(Pi/n).

Examples

			Approximations:
n ... 1-cos(Pi/n) ... 1/(1-cos(Pi/n))
1 ... 2 ............. 0.5
2 ... 1 ............. 1
3 ... 0.5 ........... 2
4 ... 0.292893 ...... 3.31421
5 ... 0.190983 ...... 5.23607
6 ... 0.133975 ...... 7.4741
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A248360.

Programs

Mathematica

z = 800; f[n_] := f[n] = Select[Range[z], Cos[Pi/#] + 1/(#*n) > 1 &, 1];
u = Flatten[Table[f[n], {n, 1, z}]]  (* A248359 *)
Table[Floor[1/(1 - Cos[Pi/n])], {n, 1, z/10}]  (* A248360 *)

Formula

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