Baum-Sweet Sequence

The Baum-Sweet sequence is the sequence of numbers  such that  if the binary representation of  contains no block of consecutive 0s of odd length, and  otherwise. For , 2, ... the first few terms are 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, ... (OEIS A086747). A recurrence plot of the limiting value of this sequence is illustrated above.

REFERENCES:

Allouche, J.-P. and Shallit, J. "Example 5.1.7 (The Baum-Sweet Sequence)." Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press, pp. 156-157, 2003.

Baum, L. E. and Sweet, M. M. "Continued Fractions of Algebraic Power Series in Characteristic 2." Ann. Math. 103, 593-610, 1976.

Sloane, N. J. A. Sequence A086747 in "The On-Line Encyclopedia of Integer Sequences."