Given a positive integer N, the task is to check if it is a Proth number. If the given number is a Proth number then print ‘YES’ otherwise print ‘NO’.
Proth Number: In mathematics, a Proth number is a positive integer of the form
n = k * 2n + 1
where k is an odd positive integer and n is a positive integer such that 2n > k .
The first few Proth numbers are –
3, 5, 9, 13, 17, 25, 33, 41, 49, ……
Input: 25 Output: YES Taking k= 3 and n= 3, 25 can be expressed in the form of (k.2n + 1) as (3.23 + 1) Input: 73 Output: NO Taking k=9 and n=3 73 can be expressed in the form of (k.2n + 1 ) as (9.23 + 1) But 23 is less than 9 (it should be greater than k to be Proth Number)
- Deduct 1 from the number. This would give a number in the form k*2n, if the given number is a proth number.
- Now, loop through all odd number starting form k=1 to n/k and check if k can divide n in such a way that ( n/k ) is a power of 2 or not.
- If found, print ‘YES’
- If no such value of k is found then Print ‘NO’
Below is the implementation of above idea
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