OFFSET
1,1
COMMENTS
Let Arch(n) = 2^(n+1)*sin(Pi/2^(n+1)) be the Archimedean approximation to Pi (Finch, pp. 17 and 23) given by a regular polygon of 2^(n+1) sides. A248347 provides insight into the manner of convergence of Arch(n) to Pi. Another provider is the fact that the least k for which Arch(k) < 1/4^n is A000027(n) = n. (For the closely related function arch, see A248355.)
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
FORMULA
a(n) ~ 6 * 4^(n+1) / Pi^3. - Vaclav Kotesovec, Oct 09 2014
EXAMPLE
n Pi - Arch(n) 1/(Pi - Arch(n))
1 0.313166... 3.1932...
2 0.0801252... 12.4805...
3 0.0201475... 49.6339...
4 0.00504416... 198.249...
5 0.0012615... 792.709...
MATHEMATICA
z = 200; p[k_] := p[k] = (2^(k + 1))*Sin[Pi/2^(k + 1)]
Table[Floor[1/(Pi - p[n])], {n, 1, z}] (* A248347 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Oct 05 2014
STATUS
approved