Check if a number can be expressed as a sum of consecutive numbers

Difficulty Level : Medium
Last Updated : 26 Mar, 2021

Given a number n, the task is to check whether it can be expressed as a sum of two or more consecutive numbers or not.
Examples:

Input  : n = 10 
Output : true
It can be expressed as sum of two consecutive
numbers 1 + 2 + 3 + 4.

Input  : n = 16  
Output : false
It cannot be expressed as sum of two consecutive
numbers.

Input  : n = 5  
Output : true
2 + 3 = 5

There is a direct and quick method to solve this. If a number is a power of two, then it cannot be expressed as a sum of consecutive numbers otherwise Yes.
The idea is based on below two facts.
1) Sum of any two consecutive numbers is odd as one of them has to be even and other odd.
2) 2ⁿ = 2^n-1 + 2^n-1
If we take a closer look at 1) and 2), we can get intuition behind the fact.
Below is implementation of above idea.

C++

// C++ program to check if a number can
// be expressed as sum of consecutive numbers
#include<bits/stdc++.h>
using namespace std;
 
// This function returns true if n can be
// expressed sum of consecutive.
bool canBeSumofConsec(unsigned int n)
{
    // We basically return true if n is a
    // power of two
    return ((n&(n-1)) && n);
}
 
// Driver code
int main()
{
    unsigned int n = 15;
    canBeSumofConsec(n)? cout << "true" :
                         cout << "false";
    return 0;
}

Java

// Java program to check if a number can
// be expressed as sum of consecutive numbers
 
class Test
{
    // This function returns true if n can be
    // expressed sum of consecutive.
    static boolean canBeSumofConsec(int n)
    {
        // We basically return true if n is a
        // power of two
        return (((n&(n-1))!=0) && n!=0);
    }
     
    // Driver method
    public static void main(String[] args)
    {
        int n = 15;
        System.out.println(canBeSumofConsec(n) ? "true" : "false");
    }
}

Python3

# Python 3 program to check if a number can
# be expressed as sum of consecutive numbers
 
 
# This function returns true if n
# can be expressed sum of consecutive.
def canBeSumofConsec(n) :
 
    # We basically return true if n is a
    # power of two
    return ((n&(n-1)) and n)
 
 
# Driver code
n = 15
if(canBeSumofConsec(n)) :
    print("true")
else :
    print("false")
     
# This code is contributed by Nikita Tiwari.

C#

// C# program to check if a number can be
// expressed as sum of consecutive numbers
using System;
 
class Test
{
    // This function returns true if n
    // can be expressed sum of consecutive.
    static bool canBeSumofConsec(int n)
    {
        // We basically return true if n is a
        // power of two
        return (((n & (n - 1)) != 0) && n != 0);
    }
     
    // Driver Code
    public static void Main()
    {
        int n = 15;
        Console.Write(canBeSumofConsec(n) ? "True" : "False");
    }
}
 
// This code is contributed by Nitin Mittal.

PHP

<?php
// php program to check if a number
// can be expressed as sum of
// consecutive numbers
 
// This function returns true if n
// can be expressed sum of consecutive.
function canBeSumofConsec($n)
{
     
    // We basically return true if n is a
    // power of two
    return (($n & ($n - 1)) && $n);
}
 
// Driver code
    $n = 15;
    if(canBeSumofConsec($n))
        echo "true" ;
    else
        echo "false";
 
// This code is contributed by
// nitin mittal.
?>

Javascript

<script>
 
// Javascript program to check if a number can
// be expressed as sum of consecutive numbers
 
 
    // This function returns true if n can be
    // expressed sum of consecutive.
    function canBeSumofConsec(n)
    {
        // We basically return true if n is a
        // power of two
        return (((n&(n-1))!=0) && n!=0);
    }
       
       
// function call
     
    let n = 15;
    document.write(canBeSumofConsec(n) ? "true" : "false");
     
</script>

Output:

True

Reference:
http://www.cut-the-knot.org/arithmetic/UnpropertyOfPowersOf2.shtml
This article is contributed by Sahil Chhabra(KILLER). If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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