OFFSET
1,1
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ Pi*sqrt(Pi*n/3). - Vaclav Kotesovec, Oct 09 2014
EXAMPLE
Approximations are shown here:
n Pi - arch(n) 1/(2n)
1 3.14159... 0.5
2 1.14159... 0.25
3 0.543516... 0.16667
4 0.313166... 0.125
5 0.202666... 0.1
6 0.141593... 0.08333
7 0.105506... 0.07143
8 0.0801252... 0.0625
a(5) = 8 because Pi - arch(8) < 1/10 < Pi - arch(7).
MATHEMATICA
z = 200; p[k_] := p[k] = k*Sin[Pi/k]; N[Table[Pi - p[n], {n, 1, z/10}]]
f[n_] := f[n] = Select[Range[z], Pi - p[#] < 1/(2 n) &, 1]
u = Flatten[Table[f[n], {n, 1, z}]] (* A248355 *)
v = Flatten[Position[Differences[u], 0]] (* A248356 *)
w = Flatten[Position[Differences[u], 1]] (* A248357 *)
f = Table[Floor[1/(Pi - p[n])], {n, 1, z}] (* A248358 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 05 2014
STATUS
approved