rational

Generate a sequence of all positive rational numbers.

Install

Use

There are two main functions: nth-rational and rational-seq.

nth-rational

Returns nth rational (0-based) as ordered by a breadth-first navigation of the Calkin-Wilf tree: 1, 1/2, 2/1, 1/3, 3/2, 2/3, 3/1, ...

Examples:

First

(nth-rational 0)
;;=> 1

Second

(nth-rational 1)
;;=> 1/2

Big Indices

(nth-rational 98254)
;;=> 179/40
(nth-rational 10000000000000000000000000000000000000000000000)
;;=> 100081852181957676623/97939718087223099718

rational-seq

Generates a lazy sequence of rational numbers following the same order as nth-rational with an optional starting index.

First 100 Rationals

Include them all:

(take 100 (rational-seq))

Skip the first 30:

(take 70 (rational-seq 30))

First Rational w/ Denominator Larger Than Max Integer Value

(->> (rational-seq 10000000000000000000)
     (filter #(cond->> % (ratio? %) denominator :else (< Integer/MAX_VALUE)))
     (take 1))
;;=> 1035723213/3048158966