FareySequence

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Wolfram's own FareySequence, mapped through for the transpiler and the oracle but not yet written up here.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageFareySequence✓↗

FareySequence(...)Wolfram's own FareySequence, mapped through for the transpiler and the oracle but not yet written up here.

Typed signatures

Type	Package	Applies
(integer) -> list	modular	always

Domain: Wolfram

Examples

Basic #

All reduced fractions in $[0,1]$ with denominator at most 5, in order

live ↗

In$\mathrm{FareySequence}(5)$Out$\bigl\lbrack0, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, 1\bigr\rbrack$

Scope #

A shorter sequence, ending at 0 and 1

live ↗

In$\mathrm{FareySequence}(3)$Out$\bigl\lbrack0, \frac{1}{3}, \frac{1}{2}, \frac{2}{3}, 1\bigr\rbrack$

Applications #

live ↗

In$\mathrm{Map}(\mathrm{Denominator}, \mathrm{FareySequence}(12))$Out$\bigl\lbrack1, 12, 11, 10, 9, 8, 7, 6, 11, 5, 9, 4, 11, 7, 10, 3, 11, 8, 5, 12, 7, 9, 11, 2, 11, 9, 7, 12, 5, 8, 11, 3, 10, 7, 11, 4, 9, 5, 11, 6, 7, 8, 9, 10, 11, 12, 1\bigr\rbrack$

Properties #

Index into a long sequence for a single term

live ↗

In$\mathrm{FareySequence}(50)[500]$Out$\frac{29}{45}$

About

Examples	4
Checked against	Wolfram Language 4 agree
Crosswalk	Wolfram Language