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A248360 Floor( 1/(1 - cos(Pi/n) ). 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

CROSSREFS

Cf. A248360.

Sequence in context: A183137 A008738 A022790 * A194238 A270192 A053034

Adjacent sequences:  A248357 A248358 A248359 * A248361 A248362 A248363

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 07 2014

STATUS

approved

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Last modified January 18 21:06 EST 2021. Contains 340262 sequences. (Running on oeis4.)