Sequences

This Elixir Module defines many useful integer sequences.

These sequences are created as Streams, which means that they are lazily evaluated.

Most of these sequences use a recurrence relation that calculates the n-th element from n-1 or other earlier known data. This means that if you only want the n-th item of a Sequence, there might be another algorithm that is faster; But if you want multiple consecutive elements of a Sequence, this module is right up your alley!

Repository: https://github.com/Qqwy/elixir-sequences

List of included sequences:

• Sequences.integers(start, step): a helper function to create any kind of lazy integer sequence with a regular step distance.
• Sequences.integers
• Sequences.positive_integers
• Sequences.odd_integers
• Sequences.even_integers
• Sequences.zeroes
• Sequences.ones
• Sequences.factorials
• Sequences.fibonacci
• Sequences.catalan
• Sequences.triangular
• Sequences.primes
• Sequences.squareroot_tuple(n): Returns a tuple with an integer part (single integer number) and decimal part (digit stream)
• Sequences.squareroot_tuple(n, num_of_digits): Returns a tuple with an integer part (single integer number) and decimal part (digit list with given length)
• Sequences.squareroot_decimals(n): Returns decimal stream of the decimal expansion of a square root.
• Sequences.squareroot_expansion/1: Returns a digit stream of the decimal expansion of a square root, including the digits of the integral part at the front.

A note on Prime numbers

There are multiple known ways to generate prime numbers. Because each of these variants might have a different (time, memory)-efficiency on different intervals, prime generation variants can be called directly:

• Sequences.Primes.trial_division

(For now, there is only this one)

Sequences.primes uses Sequences.Primes.trial_division internally. This might change in the future.

Installation

This package is available in Hex

1. Add sequences to your list of dependencies in mix.exs:

   def deps do [{:sequences, "~> 1.1.0"}] end

2. Ensure sequences is started before your application:

   def application do [applications: [:sequences]] end

Changelog

• 1.1.0: Sequences for square root expansions.
• 1.0.0: First fully-functional version.