Provides the Collatz sequence starting with the given number and ending at 1

Returns an empty list if a number less than 1 is provided

parameters

Parameters

n: Positive integer to begin the sequence at

examples

Examples

iex> collatz(2)
[2, 1]

iex> collatz(0)
[]

iex> collatz(3)
[3, 10, 5, 16, 8, 4, 2, 1]

Given the integer n, returns the length of the resulting Collatz sequence, including the starting integer

Returns zero when the provided integer is less than one. This method is optimized for calculating the length over taking the length of the resulting list of collatz/1

parameters

Parameters

n: Positive integer

examples

Examples

iex> collatz_len(2)
2

iex> collatz_len(0)
0

iex> collatz_len(3)
8

Returns a Stream that supplies the Fibonacci sequence, starting at 1

examples

Examples

iex> fibonacci() |> Enum.take(10)
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]  

Returns a list of the first n integers in the Fibonacci sequence

An empty list is returned if a number less than 1 is provided

parameters

Parameters

n: An integer, the number of digits in the sequence to retrieve

examples

Examples

iex> fibonacci(10)
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]  

Returns the integer at the nth position in the Fibonacci sequence, where the first integer in the sequence is 1

When an integer less than zero is provided, nil is returned. When zero is provided, zero is returned. All other values are computed

parameters

Parameters

n: An integer, the nth digit to retrieve from the Fibonacci sequence

examples

Examples

iex> nth_fibonacci(10)
55 

iex> nth_fibonacci(-1)
nil

iex> nth_fibonacci(0)
0