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:

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,

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

Below is the implementation of the above approach:

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

Output:

1, 2, 4, 5, 7,


Reference: https://oeis.org/A001951

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Improved By : yatinagg, Code_Mech

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