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

0,2

Links

Daniel Mondot, Table of n, a(n) for n = 0..999

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

Cf. A072398 (numerators), A000796 (Pi), A068089, A002485/A002486.

Sequence in context: A269937 A065240 A178708 * A001988 A099739 A261128

Adjacent sequences: A072396 A072397 A072398 * A072400 A072401 A072402

Keyword

easy,frac,nice,nonn

Author

Rick L. Shepherd, Jun 15 2002

Status

approved