Given a number N, the task is to check whether N is a Centered pentadecagonal number or not. If the number N is a Centered Pentadecagonal Number then print “Yes” else print “No”.
Centered Pentadecagonal Number represents a dot in the centre and other dots surrounding it in successive Pentadecagonal(15-sided polygon) layers. The first few Centered pentadecagonal numbers are 1, 16, 46 …
Input: N = 16
Second Centered pentadecagonal number is 16.
Input: N = 20
1. The Kth term of the Centered pentadecagonal number is given as:
2. As we have to check that the given number can be expressed as a Centered Pentadecagonal 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 Pentadecagonal Number.
4. Else the number N is not a Centered Pentadecagonal Number.
Below is the implementation of the above approach:
Time Complexity: O(1)
Auxiliary Space: O(1)
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