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A119015 Denominators of "Farey fraction" approximations to e. 5
0, 1, 1, 1, 1, 2, 3, 4, 7, 11, 18, 25, 32, 39, 71, 110, 181, 252, 323, 394, 465, 536, 1001, 1537, 2538, 3539, 4540, 5541, 6542, 7543, 8544, 9545, 18089, 27634, 45723, 63812, 81901, 99990, 118079, 136168, 154257, 172346, 190435, 208524, 398959, 607483 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

"Add" (meaning here to add the numerators and add the denominators, not to add the fractions) 1/0 to 1/1 to make the fraction bigger: 2/1, 3/1. Now 3/1 is too big, so add 2/1 to make the fraction smaller: 5/2, 8/3, 11/4. Now 11/4 is too small, so add 8/3 to make the fraction bigger: 19/7, ...

LINKS

Table of n, a(n) for n=0..45.

Dave Rusin, Farey fractions on sci.math [Broken link]

Dave Rusin, Farey fractions on sci.math [Cached copy]

EXAMPLE

The fractions are 1/0, 0/1, 1/1, 2/1, 3/1, 5/2, 8/3, 11/4, 19/7, ...

MATHEMATICA

f[x_, n_] := (m = Floor[x]; f0 = {m, m+1/2, m+1}; r = ({a___, b_, c_, d___} /; b < x < c) :> {b, (Numerator[b] + Numerator[c]) / (Denominator[b] + Denominator[c]), c};

Join[{m, m+1}, NestList[# /. r &, f0, n-3][[All, 2]]]);

Join[{0, 1, 1}, f[E, 43] // Denominator]

(* Jean-Fran├žois Alcover, May 18 2011 *)

CROSSREFS

For another version see A006259.

Cf. A097545, A097546 gives the similar sequence for pi. A119014 gives the numerators for this sequence.

Sequence in context: A072164 A060987 A006259 * A222329 A018145 A050195

Adjacent sequences:  A119012 A119013 A119014 * A119016 A119017 A119018

KEYWORD

easy,frac,nonn

AUTHOR

Joshua Zucker, May 08 2006

STATUS

approved

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Last modified April 14 07:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)