A072399 Denominator of best approximation to Pi with denominator <= 10^n.
1, 7, 7, 113, 113, 99532, 364913, 1725033, 78256779, 811528438, 6701487259, 6701487259, 567663097408, 2851718461558, 44485467702853, 136308121570117, 9627687726852338, 21208174623389167, 842468587426513207
Offset: 0
Examples
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%.
Links
- Daniel Mondot, Table of n, a(n) for n = 0..999
Programs
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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 *) -
PARI
for(n=0,40,print1(denominator(bestappr(Pi,10^n)),",")) \\ Finds these approximations very quickly.