A Carol number is an integer of the form 4n – 2(n+1) – 1. An equivalent formula is (2n-1)2 – 2.
An Interesting Property :
For n > 2, the binary representation of the n-th Carol number is n-2 consecutive one’s, a single zero in the middle, and n + 1 more consecutive one’s. Example, n = 4 carol number is 223 and binary of 223 is 11011111, here n-2 = 4-2 = 2 consecutive ones in starting then single 0 in middle and then n + 1 = 4 + 1 = 5 consecutive ones after it.
Given a number n, the task is to find the nth Carol Number. First, few carol numbers are -1, 7, 47, 223, 959… etc.
Input : n = 2 Output: 7 Input : n = 4 Output: 223
Time complexity: O(log n) , for pow function
Auxiliary Space: O(1)
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