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https://github.com/danielpclark/multiples

Creates enumerators that step through integers from a union of two infinite sets of multiples.
https://github.com/danielpclark/multiples

creates-enumerators enumerator iterator math mathematics palindrome union

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Creates enumerators that step through integers from a union of two infinite sets of multiples.

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# Multiples



Creates enumerators that step through integers from a union of two multiples.

A pattern from the two numbers is determined (much like two frequencies create

a pattern) and the resulting palindrome is given to a custom Enumerator for you

to use.



I've created this gem from a delightful discovery I made.  When going through all

the numbers that are multiples of two different digits a pattern comes through.

This pattern is a palindrome.  See for yourself:



```

For multiples of 3 with 5 we have.



3 5 6 9 10 12 15 18 20 21 24 25 27 30 33 35 36 39 40 42 45

3 2 1 3 1  2  3  3  2  1  3  1  2  3  3  2  1  3  1  2  3

```



The palindrome for the above differences example is `3,2,1,3,1,2,3`.  I thought this

may be true for other numbers as well so lets look at 4 with 5.



```

4 5 8 10 12 15 16 20 24 25 28 30 32 35 36 40

4 1 3 2  2  3  1  4  4  1  3  2  2  3  1  4

```



As you can see from this example another palindrome has arisen `4,1,3,2,2,3,1,4`. Upon

further study of these patterns I have also found that the palindrome will always be the

same length as the two numbers added together minus one.  So 3 and 5's palindrome is the

length `3+5-1=7` and 4 and 5's palindromes length is `4+5-1=8`.  I wrote code that tests

any two different digits and those are accurate lengths.



So if you'd like an iterator that steps through multiples without calculating every step

of the way you may use this gem for that.



### NOTES



* If one of the numbers is divisible by the other than this rule doesn't apply.

* The gem doesn't take into account zero and negative numbers.  If you wanted to you may progress backwards through negative numbers.



## Installation



Add this line to your application's Gemfile:



```ruby

gem 'multiples'

```



And then execute:



    $ bundle



Or install it yourself as:



    $ gem install multiples



## Usage



```ruby

x = Multiples.new(3,5)

x.next

# => 3



x.each do |val|

  break val if val > 14

end

# => 15



x.lazy.select {|v| v % 10 == 0}.take(2).to_a

# => [20, 30]

x.next

# => 33 

x.phase

# => 1

x.prev

# => 30

x.phase

# => 0



y = Multiples.new(3,5)



y.lazy.take(4).to_a

# => [3, 5, 6, 9] 

y.next

# => 10 

y.prev

# => 9 



y.lazy.select {|v| v % 7 == 0 }.take(14).to_a

# => [21, 35, 42, 63, 70, 84, 105, 126, 140, 147, 168, 175, 189, 210]

```



## Benchmark



If you reuse the Enumerator (rather than re-initialzing it) you will gain a

performance advantage of at least 100% (2x original).  If you create a new Enumerator each time

you use it your performance will be 30% worse than if you had not used this gem.

See the benchmark file in test/benches for an example and run `rake bench` to see

the results for yourself.



## Development



After checking out the repo, run `bin/setup` to install dependencies. Then, run `rake test` to run the tests. You can also run `bin/console` for an interactive prompt that will allow you to experiment.



To install this gem onto your local machine, run `bundle exec rake install`. To release a new version, update the version number in `version.rb`, and then run `bundle exec rake release`, which will create a git tag for the version, push git commits and tags, and push the `.gem` file to [rubygems.org](https://rubygems.org).



## Contributing



Bug reports and pull requests are welcome on GitHub at https://github.com/danielpclark/multiples.



## License



The gem is available as open source under the terms of the [MIT License](http://opensource.org/licenses/MIT).