A072398 Numerator of best approximation to Pi with denominator <= 10^n.

3, 22, 22, 355, 355, 312689, 1146408, 5419351, 245850922, 2549491779, 21053343141, 21053343141, 1783366216531, 8958937768937, 139755218526789, 428224593349304, 30246273033735921, 66627445592888887

Offset: 0

Author

Rick L. Shepherd, Jun 15 2002

Keywords

• easy
• frac
• nice
• nonn

Examples

			A072398(5) = 312689 because A072398(5)/A072399(5) = 312689/99532 is the best rational approximation to Pi with positive denominator <= 10^5 = 100000. This approximation is accurate to 0.00000000092766%.
		

Links

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

Crossrefs

Cf. A072399 (denominators), A000796 (Pi), A068089, A002485/A002486.

Programs

Mathematica

nmax = 17; cv = Convergents[Pi, 2*nmax] // Reverse; a[n_] := Select[cv, Denominator[#] <= 10^n &, 1] // Numerator // First; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jan 04 2013 *)

PARI

for(n=0,40,print1(numerator(bestappr(Pi,10^n)),",")) \\ Finds these approximations very quickly.