weekly_programmer

For Weekly Programming Challenges

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Weekly Programmer - Week 1

From Weekly Programmer Challenges

Description

In mathematics, the Baum–Sweet sequence is an infinite automatic sequence of 0s and 1s defined by the rule:

b_n = 1 if the binary representation of n contains no block of consecutive 0s of odd length;
b_n = 0 otherwise; for n >= 0.

For example, b_4 = 1 because the binary representation of 4 is 100, which only contains one block of consecutive 0s of length 2; whereas b_5 = 0 because the binary representation of 5 is 101, which contains a block of consecutive 0s of length 1. When n is 19611206, b_n is 0 because:

19611206 = 1001010110011111001000110 base 2
            00 0 0  00     00 000  0 runs of 0s
               ^ ^            ^^^    odd length sequence

Because we find an odd length sequence of 0s, b_n is 0.

Challenge Description

Your challenge today is to write a program that generates the Baum-Sweet sequence from 0 to some number n. For example, given “20” your program would emit:

1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0

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