A072398 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

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

EXAMPLE

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%.

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 *)

PROG

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

CROSSREFS

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

Sequence in context: A226028 A248626 A360366 * A134924 A042547 A269799

Adjacent sequences: A072395 A072396 A072397 * A072399 A072400 A072401

KEYWORD

easy,frac,nice,nonn

AUTHOR

Rick L. Shepherd, Jun 15 2002

STATUS

approved