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Beatty sequence

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  • Last Updated : 26 Oct, 2021

Beatty sequence (or homogeneous Beatty sequence) is the sequence of integers found by taking the floor of the positive multiples of a positive irrational number.
The Nth term of the Beatty sequence: 
 

T(i) = \lfloor N * \sqrt{2} \rfloor
 

 

Find the N terms of Beatty Sequence

Given an integer N, the task is to print the first N terms of the Beatty sequence.
Examples: 
 

Input: N = 5 
Output: 1, 2, 4, 5, 7
Input: N = 10 
Output: 1, 2, 4, 5, 7, 8, 9, 11, 12, 
 

 

Approach: The idea is to iterate from 1 to N using loop to find the i^{th}     term of the sequence. The i^{th}     term of the Beatty sequence is given by:
 

T(i) = \lfloor i * \sqrt{2} \rfloor
 

Below is the implementation of the above approach: 
 

C++




// C++ implementation of the
// above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to print the first N terms
// of the Beatty sequence
void BeattySequence(int n)
{
    for (int i = 1; i <= n; i++) {
        double ans = floor(i * sqrt(2));
        cout << ans << ", ";
    }
}
 
// Driver code
int main()
{
    int n = 5;
 
    BeattySequence(n);
 
    return 0;
}

Java




// Java implementation of the
// above approach
import java.util.*;
class GFG{
 
// Function to print the first N terms
// of the Beatty sequence
static void BeattySequence(int n)
{
    for(int i = 1; i <= n; i++)
    {
        int ans = (int)Math.floor(i * Math.sqrt(2));
        System.out.print(ans + ", ");
    }
}
 
// Driver code
public static void main(String args[])
{
    int n = 5;
 
    BeattySequence(n);
}
}
 
// This code is contributed by Code_Mech

Python3




# Python3 implementation of the
# above approach
import math
 
# Function to print the first N terms
# of the Beatty sequence
def BeattySequence(n):
    for i in range(1, n + 1):
        ans = math.floor(i * math.sqrt(2))
        print(ans, end = ', ')
 
# Driver code
n = 5
BeattySequence(n)
 
# This code is contributed by yatin

C#




// C# implementation of the
// above approach
using System;
class GFG{
 
// Function to print the first N terms
// of the Beatty sequence
static void BeattySequence(int n)
{
    for(int i = 1; i <= n; i++)
    {
       double ans = Math.Floor(i * Math.Sqrt(2));
       Console.Write(ans + ", ");
    }
}
 
// Driver code
public static void Main()
{
    int n = 5;
 
    BeattySequence(n);
}
}
 
// This code is contributed by Code_Mech

Javascript




<script>
// Javascript implementation of the
// above approach
 
    // Function to print the first N terms
    // of the Beatty sequence
    function BeattySequence( n) {
        for ( let i = 1; i <= n; i++) {
            let ans = parseInt( Math.floor(i * Math.sqrt(2)));
            document.write(ans + ", ");
        }
    }
 
    // Driver code
      
        let n = 5;
 
        BeattySequence(n);
// This code contributed by Rajput-Ji
</script>
Output: 
1, 2, 4, 5, 7,

 

Time Complexity: O(n1/2)

Auxiliary Space: O(1)

Reference: https://oeis.org/A001951
 


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