Beatty序列

Beatty序列(或齐次Beatty序列)是通过取正无理数的正倍数的底数而找到的整数序列。
Beatty序列的第N^个术语：

$T(i) = \lfloor N * \sqrt{2} \rfloor$
 

查找Beatty序列的N个项

给定整数N ，任务是打印Beatty序列的前N个项。
例子：

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

方法：想法是使用循环从1迭代到N以找到$i^{th}$序列项。这$i^{th}$ Beatty序列的项由下式给出：

$T(i) = \lfloor i * \sqrt{2} \rfloor$
 

下面是上述方法的实现：

C++

// C++ implementation of the
// above approach
 
#include 
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

// Javascript implementation of the
// above approach
 
    // Function to prlet 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

输出：

1, 2, 4, 5, 7,

参考： https : //oeis.org/A001951