Python Program to find the nth Kynea number

By Abinash Reddy

In this article, we will learn how to find the nth Kynea number in Python. But first, let’s discuss a few points about Kynea number.

What is Kynea number?

In mathematical, Kynea number is an integer of the form

where n is a positive integer. Which is equivalent to . To learn more about Kynea number click here.

The first few Kynea numbers are

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

Find the nth Kynea number in Python

Method 1:

Directly applying the formulae to given input n. Python has an inbuilt function pow() to calculate the power of any value.

def kynea_number(n):
    result = 0
    result = (pow(2,n)+1)**2 - 2
    return result
n = int(input("Enter the n value: "))
print("The nth kynea number is ", kynea_number(n))

Output

Enter the n value: 8
The nth kynea number is 66047

Enter the n value: 21
The nth kynea number is 4398050705407

Time complexity: O(1)

Space complexity: O(1)

Method 2: Using Bitwise shift

The value of 2^n is equivalent to 1<<n. So we are going to use 1<<n instead of 2^n and apply the formulae .

def kynea_number(n):
    # calculate 2^n+1
    n = (1<<n)+1
    # (2^n+1)^2
    n = n*n
    # ((2^n+1)^2)-2
    n = n-2
    return n
n = int(input("Enter the n value: "))
print("The nth kynea number is ", kynea_number(n))

Output

Enter the n value: 7
The nth kynea number is 16639

Enter the n value: 6
The nth kynea number is 4223

Time complexity: O(1)

Space complexity: O(1)

Also, read

• Generating first ten numbers of Pell series in Python
• Binomial Theorem Python – Printing the Binomial Series