login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324797 Irregular triangle read by rows: row n gives denominators of fractions in the Farey subsequence B(m). 2
1, 2, 1, 1, 3, 2, 3, 1, 1, 4, 3, 5, 2, 5, 3, 4, 1, 1, 5, 4, 3, 5, 7, 2, 7, 5, 3, 4, 5, 1, 1, 6, 5, 4, 7, 3, 8, 5, 7, 9, 2, 9, 7, 5, 8, 3, 7, 4, 5, 6, 1, 1, 7, 6, 5, 4, 7, 3, 8, 5, 7, 9, 11, 2, 11, 9, 7, 5, 8, 3, 7, 4, 5, 6, 7, 1, 1, 8, 7, 6, 5, 9, 4, 7, 10, 3, 11, 8, 5, 12, 7, 9, 11, 13, 2, 13, 11, 9, 7, 12, 5, 8, 11, 3, 10, 7, 4, 9, 5, 6, 7, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

B(n) is denoted by F(B(2n),n) in Matveev (2017) - see definition on page 1. B(n) consists of the terms h/k of the Farey series F_{2n} such that k-n <= h <= n.

A049691 gives the row lengths.

REFERENCES

A. O. Matveev, Farey Sequences, De Gruyter, 2017.

LINKS

Table of n, a(n) for n=1..113.

EXAMPLE

The first few sequences B(1), B(2), B(3), B(4) are:

[0, 1/2, 1],

[0, 1/3, 1/2, 2/3, 1],

[0, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 1],

[0, 1/5, 1/4, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3, 3/4, 4/5, 1], [0, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 4/9, 1/2, 5/9, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 1],

...

MAPLE

Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end:

B := proc(m) local a, i, h, k; global Farey; a:=[];

for i in Farey(2*m) do

h:=numer(i); k:=denom(i);

if (h <= m) and (k-m <= h) then a:=[op(a), i]; fi; od: a; end;

CROSSREFS

Cf. A006842/A006843, A049691, A324796 (numerators).

Sequence in context: A153901 A132844 A006843 * A049456 A117506 A179205

Adjacent sequences:  A324794 A324795 A324796 * A324798 A324799 A324800

KEYWORD

nonn,frac,tabf,changed

AUTHOR

N. J. A. Sloane, Sep 10 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 26 14:08 EST 2020. Contains 331280 sequences. (Running on oeis4.)