project_euler.problem_047.sol1
==============================

.. py:module:: project_euler.problem_047.sol1

.. autoapi-nested-parse::

   Combinatoric selections

   Problem 47

   The first two consecutive numbers to have two distinct prime factors are:

   14 = 2 x 7
   15 = 3 x 5

   The first three consecutive numbers to have three distinct prime factors are:

   644 = 2² x 7 x 23
   645 = 3 x 5 x 43
   646 = 2 x 17 x 19.

   Find the first four consecutive integers to have four distinct prime factors each.
   What is the first of these numbers?



Functions
---------

.. autoapisummary::

   project_euler.problem_047.sol1.equality
   project_euler.problem_047.sol1.run
   project_euler.problem_047.sol1.solution
   project_euler.problem_047.sol1.unique_prime_factors
   project_euler.problem_047.sol1.upf_len


Module Contents
---------------

.. py:function:: equality(iterable: list) -> bool

   Check the equality of ALL elements in an iterable
   >>> equality([1, 2, 3, 4])
   False
   >>> equality([2, 2, 2, 2])
   True
   >>> equality([1, 2, 3, 2, 1])
   False


.. py:function:: run(n: int) -> list[int]

   Runs core process to find problem solution.
   >>> run(3)
   [644, 645, 646]


.. py:function:: solution(n: int = 4) -> int | None

   Return the first value of the first four consecutive integers to have four
   distinct prime factors each.
   >>> solution()
   134043


.. py:function:: unique_prime_factors(n: int) -> set

   Find unique prime factors of an integer.
   Tests include sorting because only the set matters,
   not the order in which it is produced.
   >>> sorted(set(unique_prime_factors(14)))
   [2, 7]
   >>> sorted(set(unique_prime_factors(644)))
   [2, 7, 23]
   >>> sorted(set(unique_prime_factors(646)))
   [2, 17, 19]


.. py:function:: upf_len(num: int) -> int

   Memoize upf() length results for a given value.
   >>> upf_len(14)
   2