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 A327361 Minimal denominator among the fractions with n-digit numerator and n-digit denominator that best approximate Pi. 2
 1, 14, 113, 1017, 31746, 265381, 1725033, 25510582, 209259755, 1963319607, 13402974518, 313006581566, 2851718461558, 30226875395063, 136308121570117, 1952799169684491, 21208174623389167, 136876735467187340, 1684937174853026414, 10109623049118158484 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES O. Zelenyak, Programming workshop on Turbo Pascal: Tasks, Algorithms and Solutions, Litres, 2018, page 255. (Provides first 8 terms. Also contains similar sequences for sqrt(2) and e.) LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..1000 O. Zelenyak, Programming workshop on Turbo Pascal: Tasks, Algorithms and Solutions, Litres, 2018, page 255. EXAMPLE The fractions with 2-digit numerators and 2-digit denominators that best approximate Pi are 44/14 and 88/28. The fraction with 6-digit numerator and 6-digit denominator that best approximates Pi is 833719/265381. MATHEMATICA (* Given the 8th term, find the 9th term *) (* This took twelve-plus hours to run on a laptop *) ResultList = {}; nVal = 9; tol = Abs[80143857/25510582 - Pi]; (* 80143857 is A327360(8), 25510582 is A327361(8) *) Do[   CurrentNumerator = i;   Do[    CurrentDenominator = j;    CurrentQuotient = N[CurrentNumerator/CurrentDenominator];    If[     Abs[CurrentQuotient - Pi] <= tol,     ResultList = Append[ResultList, {CurrentNumerator, CurrentDenominator}]     ],    {j, Floor[i/(Pi + tol)], Floor[i/(Pi - tol)] + 1}],   {i, Floor[(Pi - tol)*10^(nVal - 1)], (10^nVal - 1)}]; DifferenceList =   Table[    Abs[ResultList[[i, 1]]/ResultList[[i, 2]] - Pi],    {i, 1, Length[ResultList]}]; Extract[ResultList, Position[DifferenceList, Min[DifferenceList]]] CROSSREFS A327360 gives the corresponding numerators. Cf. A072398/A072399, which gives the best rational approximation to Pi subject to a different constraint. Cf. A002485/A002486, A063674/A063673, A325158/A325159. Sequence in context: A155655 A007817 A285147 * A293874 A044346 A044727 Adjacent sequences:  A327358 A327359 A327360 * A327362 A327363 A327364 KEYWORD base,frac,nonn,more AUTHOR Jason Zimba, Sep 03 2019 EXTENSIONS a(10)-a(20) from Jon E. Schoenfield, Mar 12 2021 STATUS approved

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Last modified October 28 10:01 EDT 2021. Contains 348327 sequences. (Running on oeis4.)