Given a number N, the task is to check if N is a Centered Pentagonal Number or not. If the number N is a Centered Pentagonal Number then print “Yes” else print “No”.
Centered Pentagonal Number is a centered figurate number that represents a pentagon with a dot in the centre and other dots surrounding it in pentagonal layers successively. The first few Centered Pentagonal Number are 1, 6, 16, 31, 51, 76, 106 …
Input: N = 6
Second Centered pentagonal number is 6.
Input: N = 20
1. The Kth term of the Centered Pentagonal Number is given as
2. As we have to check that the given number can be expressed as a Centered Pentagonal Number or not. This can be checked as:
3. If the value of K calculated using the above formula is an integer, then N is a Centered Pentagonal Number.
4. Else the number N is not a Centered Pentagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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