The Baum-Sweet sequence is the sequence of numbers for nonnegative
integer
such that
if the binary expansion of contains no block of consecutive 0s of odd
length, and
otherwise. Taking the binary expansion of 0 to
be the single digit 0 gives , as in the cited OEIS sequence. A common alternative convention
sets ,
as in the original power series of Baum and Sweet
(1976). 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 first 128 positive-index terms is illustrated above.
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. https://doi.org/10.2307/1970953.Sloane,
N. J. A. Sequence A086747 in "The
On-Line Encyclopedia of Integer Sequences."
for nonnegative
integer 
such that 
if the binary expansion of 
contains no block of consecutive 0s of odd
length, and 
otherwise. Taking the binary expansion of 0 to
be the single digit 0 gives 
, as in the cited OEIS sequence. A common alternative convention
sets 
,
as in the original power series of Baum and Sweet
(1976). 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 first 128 positive-index terms is illustrated above.
