Baum Sweet Sequence
Baum Sweet Sequence is an infinite binary sequence of 0s and 1s. The nth term of the sequence is 1 if the number n has no odd number of contiguous zeroes in its binary representation, else the nth term is 0.
The first few terms of the sequence are: b1 = 1 (binary of 1 is 1) b2 = 0 (binary of 2 is 10) b3 = 1 (binary of 3 is 11) b4 = 1 (binary of 4 is 100) b5 = 0 (binary of 5 is 101) b6 = 0 (binary of 6 is 110)
Given a natural number n. The task is to find the nth term of the Baum Sweet sequence, i.e, check whether it contains any consecutive block of zeroes of odd length.
Input: n = 8 Output: 0 Explanations: Binary representation of 8 is 1000. It contains odd length block of consecutive 0s. Therefore B8 is 0. Input: n = 5 Output: 1 Input: n = 7 Output: 0
The idea is to run a loop through the binary representation of n and count the length of all the consecutive zero blocks present. If there is at-least one odd length zero block, then the nth term for the given input n is 0 else it is 1.