



import math





def 		a__      (		_UpperCamelCase      :			int				):

   if not isinstance(_UpperCamelCase			,_UpperCamelCase				):
      __lowerCamelCase    				=     F"""Input value of [number={number}] must be an integer"""
      raise TypeError(_UpperCamelCase				)

   if number < 1:
      __lowerCamelCase    				=     F"""Input value of [number={number}] must be > 0"""
      raise ValueError(_UpperCamelCase				)
   elif number == 1:
      return 3
   elif number == 2:
      return 5
   else:
      __lowerCamelCase    				=     int(math.log(number // 3			,2				)				) + 2

      __lowerCamelCase    				=     [3, 5]
      __lowerCamelCase    				=     2
      __lowerCamelCase    				=     3
      for block in range(1			,_UpperCamelCase				):
         for _ in range(_UpperCamelCase				):
            proth_list.append(2 ** (block + 1) + proth_list[proth_index - 1]				)
            proth_index += 1
         increment *= 2

   return proth_list[number - 1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  for number in range(11):
    a_								=       0
    try:
      a_								=       proth(number)
    except ValueError:
      print(f"ValueError: there is no {number}th Proth number")
      continue

    print(f"The {number}th Proth number: {value}")











from __future__ import annotations





def 		a__      (		_UpperCamelCase      :			int | float | str			,_UpperCamelCase      :			int | float | str				):
   if nth_term == "":
      return [""]
   __lowerCamelCase    				=     int(_UpperCamelCase				)
   __lowerCamelCase    				=     int(_UpperCamelCase				)
   __lowerCamelCase    				=     []
   for temp in range(int(_UpperCamelCase				)				):
      series.append(F"""1 / {pow(temp + 1			,int(_UpperCamelCase				)				)}""" if series else '''1'''				)
   return series


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  a_								=       int(input("""Enter the last number (nth term) of the P-Series"""))
  a_								=       int(input("""Enter the power for  P-Series"""))
  print("""Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p""")
  print(p_series(nth_term, power))






