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A248421
Floor( 1/(n*tan(Pi/n) - Pi) ).
4
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2014
STATUS
approved