OFFSET
3,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 3..2000
FORMULA
a(n) ~ Pi * sqrt(Pi*n/3). - Vaclav Kotesovec, Oct 09 2014
EXAMPLE
Approximations:
n ... k*tan(Pi/k)-Pi ... 1/n
3 ... 2.05456 .......... 0.33333
4 ... 0.85840 .......... 0.25
5 ... 0.49112 .......... 0.2
6 ... 0.32250 .......... 0.16666
7 ... 0.22943 .......... 0.14285
a(4) = 7 because 7*tan(Pi/7) < 1/4 < 6*tan(Pi/6).
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 *)
Differences[u]
Flatten[Position[Differences[u], 0]] (* A248419 *)
Flatten[Position[Differences[u], 1]] (* A248420 *)
Table[Floor[1/(p[n] - Pi)], {n, 3, z}] (* A248421 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2014
STATUS
approved