Python Program to find the nth Kynea Number

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Given the number n, the task is to print nth Kynea Number in Python.

Kynea number is a mathematical integer of the type

nth = 4^n + 2^(n + 1) – 1, where n is a positive integer.

Which can be also written as

 

The initial Kynea numbers are

7, 23, 79, 287, 1087, 4223, 16639,…………..

Examples:

Example1:

Input:

Given nth number =6

Output:

The nth Kynea number = 4223

Example2:

Input:

Given nth number =8

Output:

The nth Kynea number = 66047

Python Program to find the nth Kynea Number

Below are the ways to program to find the nth Kynea Number.

Method #1: Using ** operator (Static Input)

Approach:

  • Give the number n as static input and store it in a variable.
  • Calculate the power of 2^n using the ** operator and store it in another variable say partialres.
  • Calculate the value of (partialres+1)^2-2 using ** and arithmetic operators.
  • Print the result.
  • The Exit of the Program.

Below is the implementation:

# Give the number n as static input and store it in a variable.
nthNum = 6
# Calculate the power of 2^n using the ** operator
# and store it in another variable say partialres.
partialres = 2**nthNum
# Calculate the value of (partialres+1)^2-2 
# using ** and arithmetic operators.
nthresult = (partialres+1)**2-2
# Print the result.
print('The nth Kynea number =', nthresult)

Output:

The nth Kynea number = 4223

Method #2: Using ** operator (User Input)

Approach:

  • Give the number n as user input using int(input()) and store it in a variable.
  • Calculate the power of 2^n using the ** operator and store it in another variable say partialres.
  • Calculate the value of (partialres+1)^2-2 using ** and arithmetic operators.
  • Print the result.
  • The Exit of the Program.

Below is the implementation:

# Give the number n as user input using int(input()) and store it in a variable.
nthNum = int(input('Enter some random nth Number = '))
# Calculate the power of 2^n using the ** operator
# and store it in another variable say partialres.
partialres = 2**nthNum
# Calculate the value of (partialres+1)^2-2 
# using ** and arithmetic operators.
nthresult = (partialres+1)**2-2
# Print the result.
print('The nth Kynea number =', nthresult)

Output:

Enter some random nth Number = 9
The nth Kynea number = 263167

Method #3: Using pow operator (Static Input)

Approach:

  • Give the number n as static input and store it in a variable.
  • Calculate the power of 2^n using the pow function and store it in another variable say partialres.
  • Calculate the value of (partialres+1)^2-2 using the pow function and arithmetic operators.
  • Print the result.
  • The Exit of the Program.

Below is the implementation:

# Give the number n as static input and store it in a variable.
nthNum = 6
# Calculate the power of 2^n using the pow function
# and store it in another variable say partialres.
partialres = 2**nthNum
# Calculate the value of (partialres+1)^2-2 
# using pow function and arithmetic operators.
nthresult = (partialres+1)**2-2
# Print the result.
print('The nth Kynea number =', nthresult)

Output:

The nth Kynea number = 4223

Method #4: Using pow operator (User Input)

Approach:

  • Give the number n as user input using int(input()) and store it in a variable.
  • Calculate the power of 2^n using the pow function and store it in another variable say partialres.
  • Calculate the value of (partialres+1)^2-2 using the pow function and arithmetic operators.
  • Print the result.
  • The Exit of the Program.

Below is the implementation:

# Give the number n as user input using int(input()) and store it in a variable.
nthNum = int(input('Enter some random nth Number = '))
# Calculate the power of 2^n using the pow function
# and store it in another variable say partialres.
partialres = 2**nthNum
# Calculate the value of (partialres+1)^2-2 
# using pow function and arithmetic operators.
nthresult = (partialres+1)**2-2
# Print the result.
print('The nth Kynea number =', nthresult)

Output:

Enter some random nth Number = 8
The nth Kynea number = 66047

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