OFFSET
1,1
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
Jon E. Schoenfield, Magma program
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;
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
KEYWORD
base,frac,nonn
AUTHOR
Jason Zimba, Sep 03 2019
EXTENSIONS
Terms a(10) and beyond from Jon E. Schoenfield, Mar 11 2021
STATUS
approved