Add algorithm for creating Hamming numbers (#4992)

* Added algorithm for creating Hamming numbers series in Python

* Changed to f-string format.

* Added modifications

* Update and rename hamming.py to hamming_numbers.py

* Update hamming_numbers.py

* Update hamming_numbers.py

* Rename maths/series/hamming_numbers.py to maths/hamming_numbers.py

Co-authored-by: John Law <johnlaw.po@gmail.com>

maths/hamming_numbers.py

@@ -0,0 +1,51 @@
+"""
+A Hamming number is a positive integer of the form 2^i*3^j*5^k, for some
+non-negative integers i, j, and k. They are often referred to as regular numbers.
+More info at: https://en.wikipedia.org/wiki/Regular_number.
+"""
+
+
+def hamming(n_element: int) -> list:
+    """
+    This function creates an ordered list of n length as requested, and afterwards
+    returns the last value of the list. It must be given a positive integer.
+
+    :param n_element: The number of elements on the list
+    :return: The nth element of the list
+
+    >>> hamming(5)
+    [1, 2, 3, 4, 5]
+    >>> hamming(10)
+    [1, 2, 3, 4, 5, 6, 8, 9, 10, 12]
+    >>> hamming(15)
+    [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
+    """
+    n_element = int(n_element)
+    if n_element < 1:
+        my_error = ValueError("a should be a positive number")
+        raise my_error
+
+    hamming_list = [1]
+    i, j, k = (0, 0, 0)
+    index = 1
+    while index < n_element:
+        while hamming_list[i] * 2 <= hamming_list[-1]:
+            i += 1
+        while hamming_list[j] * 3 <= hamming_list[-1]:
+            j += 1
+        while hamming_list[k] * 5 <= hamming_list[-1]:
+            k += 1
+        hamming_list.append(
+            min(hamming_list[i] * 2, hamming_list[j] * 3, hamming_list[k] * 5)
+        )
+        index += 1
+    return hamming_list
+
+
+if __name__ == "__main__":
+    n = input("Enter the last number (nth term) of the Hamming Number Series: ")
+    print("Formula of Hamming Number Series => 2^i * 3^j * 5^k")
+    hamming_numbers = hamming(int(n))
+    print("-----------------------------------------------------")
+    print(f"The list with nth numbers is: {hamming_numbers}")
+    print("-----------------------------------------------------")