# Python Program to find the nth Kynea number

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)

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