Thabit number

Given a positive integer n, the task is to check if it is a Thabit number. If the given number is a Thabit number then print ‘YES’ otherwise print ‘NO’.
Thabit number: In mathematics, a Thabit Number is a positive integer of form 3* 2ⁿ – 1, where n is a non-negative integer.
The first few Thabit numbers are – 
2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 

Examples: 

Input: 47 
Output: YES 
Explanation: for n=4, 47 can be expressed in the form of 3.2ⁿ -1 as 3.2⁴ -1.

Input: 65 
Output: NO 
Explanation: No such value of n exist for which 65 can be expressed in the form of 3.2ⁿ – 1 

Approach : 

1. Add 1 to the given number, Now the number must be of the form 3*2ⁿ
2. Divide the number by 3, By now the number must be of the form 2ⁿ
3. Check if the number is a power of 2 or not, To check if the number is power of two or not refer this .
4. If the number is power of 2 then Print ‘YES’ otherwise ‘NO’.

C++

// CPP program to check if a given
// number is Thabit number or not.
#include <bits/stdc++.h>
using namespace std;

// Utility function to check power of two
bool isPowerOfTwo(int n)
{
    return (n && !(n & (n - 1)));
}

// function to check if the given number
// is Thabit Number
bool isThabitNumber(int n)
{
    // Add 1 to the number
    n = n + 1;

    // Divide the number by 3
    if (n % 3 == 0)
        n = n / 3;
    else
        return false;

    // Check if the given number is power of 2
    if (isPowerOfTwo(n))
        return true;

    else
        return false;
}

// Driver Program
int main()
{
    int n = 47;
    if (isThabitNumber(n))
        cout << "YES";
    else
        cout << "NO";

    return 0;
}

Java

// Java code to check
// for thabit number

class GFG {

    // Utility function to check power of two
    static boolean isPowerOfTwo(int n)
    {
        return n != 0 && ((n & (n - 1)) == 0);
    }

    // function to check if the given number
    // is Thabit Number
    static boolean isThabitNumber(int n)
    {
        // Add 1 to the number
        n = n + 1;

        // Divide the number by 3
        if (n % 3 == 0)
            n = n / 3;
        else
            return false;

        // Check if the given number is power of 2
        if (isPowerOfTwo(n))
            return true;

        else
            return false;
    }

    // Driver Program
    public static void main(String[] args)
    {
        int n = 47;

        // Check if number is
        // thabit number

        if (isThabitNumber(n)) {
            System.out.println("YES");
        }
        else {
            System.out.println("NO");
        }
    }
}

Python3

# Python code to check
# thabit number

# Utility function to Check
# power of two

def isPowerOfTwo(n):

    return (n and (not(n & (n - 1))))


# function to check if the given number
# is Thabit Number
def isThabitNumber( n ):

    # Add 1 to the number
    n = n + 1;

    # Divide the number by 3
    if (n % 3 == 0):
        n = n//3;
    else:
       return False


    # Check if the given number
    # is power of 2
    if (isPowerOfTwo(n)):
        return True

    else:
         return False


# Driver Program
n = 47

# Check if number is
# thabit number
if (isThabitNumber(n)):
    print("YES")
else:
    print("NO")

C#

// C# code to check
// thabit number

using System;
class GFG {

    // Utility function to check power of two
    static bool isPowerOfTwo(int n)
    {
        return n != 0 && ((n & (n - 1)) == 0);
    }

    // function to check if the given number
    // is Thabit Number
    static bool isThabitNumber(int n)
    {
        // Add 1 to the number
        n = n + 1;

        // Divide the number by 3
        if (n % 3 == 0)
            n = n / 3;
        else
            return false;

        // Check if the given number is power of 2
        if (isPowerOfTwo(n))
            return true;

        else
            return false;
    }
    // Driver Program
    public static void Main()
    {
        int n = 47;

        // Check if number is
        // thabit number

        if (isThabitNumber(n)) {
            Console.WriteLine("YES");
        }
        else {
            Console.WriteLine("NO");
        }
    }
}

PHP

<?php
// PHP program to check if a given
// number is Thabit number or not.

// Utility function to check
// power of two
function isPowerOfTwo($n)
{
    return ($n && !($n & ($n - 1)));
}

// function to check if the
// given number is Thabit Number
function isThabitNumber($n)
{
    // Add 1 to the number
    $n = $n + 1;

    // Divide the number by 3
    if ($n % 3 == 0)
        $n = $n / 3;
    else
        return false;

    // Check if the given number
    // is power of 2
    if (isPowerOfTwo($n))
        return true;

    else
        return false;
}

// Driver Code
$n = 47;
if (isThabitNumber($n))
    echo "YES";
else
    echo "NO";

// This code is contributed
// by Shashank
?>

Javascript

<script>

// Javascript program to check if a given
// number is Thabit number or not.

// Utility function to check power of two
function isPowerOfTwo(n)
{
    return (n && !(n & (n - 1)));
}

// function to check if the given number
// is Thabit Number
function isThabitNumber(n)
{
    // Add 1 to the number
    n = n + 1;

    // Divide the number by 3
    if (n % 3 == 0)
        n = n / 3;
    else
        return false;

    // Check if the given number is power of 2
    if (isPowerOfTwo(n))
        return true;

    else
        return false;
}

// Driver Program
var n = 47;
if (isThabitNumber(n))
    document.write( "YES");
else
    document.write("NO");

</script>

Output:

YES

Time Complexity: O(1), as only constant operations are performed.
Auxiliary Space: O(1) as no extra space is used.