|
|
A072399
|
|
Denominator of best approximation to Pi with denominator <= 10^n.
|
|
7
|
|
|
1, 7, 7, 113, 113, 99532, 364913, 1725033, 78256779, 811528438, 6701487259, 6701487259, 567663097408, 2851718461558, 44485467702853, 136308121570117, 9627687726852338, 21208174623389167, 842468587426513207
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
EXAMPLE
|
a(6) = 364913 because A072398(6)/a(6) = 1146408/364913 is the best rational approximation to Pi with positive denominator <= 10^6 = 1000000. This approximation is accurate to 0.000000000051271%.
|
|
MATHEMATICA
|
nmax = 18; cv = Convergents[Pi, 2*nmax] // Reverse; a[n_] := Select[cv, Denominator[#] <= 10^n &, 1] // Denominator // First; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jan 04 2013 *)
|
|
PROG
|
(PARI) for(n=0, 40, print1(denominator(bestappr(Pi, 10^n)), ", ")) \\ Finds these approximations very quickly.
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,frac,nice,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|