# 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.

Thefirst few termsof the sequence are: b_{1}= 1 (binary of 1 is 1) b_{2}= 0 (binary of 2 is 10) b_{3}= 1 (binary of 3 is 11) b_{4}= 1 (binary of 4 is 100) b_{5}= 0 (binary of 5 is 101) b_{6}= 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: 0Binary representation of 8 is 1000. It contains odd length block of consecutive 0s. Therefore BExplanations:_{8}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.

`// CPP code to find the nth term of the ` `// Baum Sweet Sequence ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `nthBaumSweetSeq(` `int` `n) ` `{ ` ` ` `// bitset stores bitwise representation ` ` ` `bitset<32> bs(n); ` ` ` ` ` `// len stores the number of bits in the ` ` ` `// binary of n. builtin_clz() function gives ` ` ` `// number of zeroes present before the ` ` ` `// leading 1 in binary of n ` ` ` `int` `len = 32 - __builtin_clz(n); ` ` ` ` ` `int` `baum = 1; ` `// nth term of baum sequence ` ` ` `for` `(` `int` `i = 0; i < len;) { ` ` ` `int` `j = i + 1; ` ` ` ` ` `// enter into a zero block ` ` ` `if` `(bs[i] == 0) { ` ` ` `int` `cnt = 1; ` ` ` ` ` `// loop to run through each zero block ` ` ` `// in binary representation of n ` ` ` `for` `(j = i + 1; j < len; j++) { ` ` ` ` ` `// counts consecutive zeroes ` ` ` `if` `(bs[j] == 0) ` ` ` `cnt++; ` ` ` `else` ` ` `break` `; ` ` ` `} ` ` ` ` ` `// check if the number of consecutive ` ` ` `// zeroes is odd ` ` ` `if` `(cnt % 2 == 1) ` ` ` `baum = 0; ` ` ` `} ` ` ` `i = j; ` ` ` `} ` ` ` ` ` `return` `baum; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 8; ` ` ` `cout << nthBaumSweetSeq(n); ` ` ` `return` `0; ` `} ` |

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**Output:**

0

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