Beatty sequence

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

1, 2, 4, 5, 7,

Reference: https://oeis.org/A001951

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Improved By : yatinagg, Code_Mech

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