Adding the function is_proth_number (TheAlgorithms#12399)

* Adding the function isProthNumber(n : int) which returns true if n is a Proth number * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fixing the issues of the isprothnumber function * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * New fixes on isprothnumber() * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fixes on isprothnumber() * Fixes on isprothnumber * Fixes on isprothnumber() * Fixes on isprothnumber * Update proth_number.py * Update proth_number.py * Update proth_number.py * Update proth_number.py * Update proth_number.py * Update proth_number.py * Update proth_number.py * Update proth_number.py --------- Co-authored-by: Juanitoupipou <juan.dupierris@imt-atlantique.net> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

Author: 4 people

maths/special_numbers/proth_number.py

@@ -59,6 +59,50 @@ def proth(number: int) -> int:
  return proth_list[number - 1]
 
 
+def is_proth_number(number: int) -> bool:
+ """
+ :param number: positive integer number
+ :return: true if number is a Proth number, false otherwise
+ >>> is_proth_number(1)
+ False
+ >>> is_proth_number(2)
+ False
+ >>> is_proth_number(3)
+ True
+ >>> is_proth_number(4)
+ False
+ >>> is_proth_number(5)
+ True
+ >>> is_proth_number(34)
+ False
+ >>> is_proth_number(-1)
+ Traceback (most recent call last):
+ ...
+ ValueError: Input value of [number=-1] must be > 0
+ >>> is_proth_number(6.0)
+ Traceback (most recent call last):
+ ...
+ TypeError: Input value of [number=6.0] must be an integer
+ """
+ if not isinstance(number, int):
+ message = f"Input value of [{number=}] must be an integer"
+ raise TypeError(message)
+
+ if number <= 0:
+ message = f"Input value of [{number=}] must be > 0"
+ raise ValueError(message)
+
+ if number == 1:
+ return False
+
+ number -= 1
+ n = 0
+ while number % 2 == 0:
+ n += 1
+ number //= 2
+ return number < 2**n
+
+
 if __name__ == "__main__":
  import doctest
 
@@ -73,3 +117,9 @@ def proth(number: int) -> int:
  continue
 
  print(f"The {number}th Proth number: {value}")
+
+ for number in [1, 2, 3, 4, 5, 9, 13, 49, 57, 193, 241, 163, 201]:
+ if is_proth_number(number):
+ print(f"{number} is a Proth number")
+ else:
+ print(f"{number} is not a Proth number")