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Hilbert Number

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Given a positive integer n, the task is to print nth Hilbert Number.
Hilbert Number: In mathematics, A Hilbert Number is a positive integer of the form 4*n + 1 , Where n is a non-negative integer.
The first few Hilbert numbers are – 
 

1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97 

Examples : 

Input: 5
Output: 21 ( i.e 4*5 + 1 ) 

Input: 9
Output: 37 (i.e 4*9 + 1 )

Approach
 

  • The n-th Hilbert Number of the sequence can be obtained by putting the value of n in the formula 4*n + 1.

Below is the implementation of the above idea:
 

CPP




// CPP program to find
// nth hilbert Number
 
#include <bits/stdc++.h>
using namespace std;
 
// Utility function to return
// Nth Hilbert Number
long nthHilbertNumber(int n)
{
 
    return 4 * (n - 1) + 1;
}
 
// Driver code
int main()
{
 
    int n = 5;
 
    cout << nthHilbertNumber(n);
 
    return 0;
}


JAVA




// JAVA program to find
// nth hilbert Number
 
class GFG {
    // Utility function to return
    // Nth Hilbert Number
    static long nthHilbertNumber(int n)
    {
 
        return 4 * (n - 1) + 1;
    }
 
    // Driver code
    public static void main(String[] args)
    {
 
        int n = 5;
 
        System.out.println(nthHilbertNumber(n));
    }
}


Python




# Python3 program to find
# nth hilbert Number
 
 
# Utility function to return
# Nth Hilbert Number
def nthHilbertNumber( n):
         
    return 4*(n-1) + 1
     
# Driver code
 
n = 5
 
print(nthHilbertNumber(n))


C#




// C# program to find
// nth hilbert Number
 
using System;
class GFG {
    // Utility function to return
    // Nth Hilbert Number
    static long nthHilbertNumber(int n)
    {
 
        return 4 * (n - 1) + 1;
    }
 
    // Driver code
    public static void Main()
    {
 
        int n = 5;
 
        Console.WriteLine(nthHilbertNumber(n));
    }
}


PHP




<?php
// Python3 program to find
// nth hilbert Number
 
 
// Utility function to return
// Nth Hilbert Number
function nthHilbertNumber($n)
{
         
    return 4*($n-1) + 1;
  
}
 
// Driver code
 
$n=5;
 
echo nthHilbertNumber($n);
 
?>


Javascript




<script>
 
// Javascript program to find
// nth hilbert Number
 
// Utility function to return
// Nth Hilbert Number
function nthHilbertNumber(n)
{
 
    return 4 * (n - 1) + 1;
}
 
// Driver code
var n = 5;
document.write( nthHilbertNumber(n));
 
// This code is contributed by noob2000.
</script>


Output: 

17

 

Time Complexity: O(1), performing constant multiplication and addition operations.
Auxiliary Space: O(1) because using constant space.



Last Updated : 26 Aug, 2022
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