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,
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 <bits/stdc++.h>using namespace std;// Function to print the first N terms// of the Beatty sequencevoid BeattySequence(int n){ for (int i = 1; i <= n; i++) { double ans = floor(i * sqrt(2)); cout << ans << ", "; }}// Driver codeint main(){ int n = 5; BeattySequence(n); return 0;} |
Java
// Java implementation of the// above approachimport java.util.*;class GFG{// Function to print the first N terms// of the Beatty sequencestatic 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 codepublic static void main(String args[]){ int n = 5; BeattySequence(n);}}// This code is contributed by Code_Mech |
Python3
# Python3 implementation of the# above approachimport math# Function to print the first N terms# of the Beatty sequencedef BeattySequence(n): for i in range(1, n + 1): ans = math.floor(i * math.sqrt(2)) print(ans, end = ', ')# Driver coden = 5BeattySequence(n)# This code is contributed by yatin |
C#
// C# implementation of the// above approachusing System;class GFG{// Function to print the first N terms// of the Beatty sequencestatic void BeattySequence(int n){ for(int i = 1; i <= n; i++) { double ans = Math.Floor(i * Math.Sqrt(2)); Console.Write(ans + ", "); }}// Driver codepublic 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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