Baum-Sweet Sequence
المؤلف:
Allouche, J.-P. and Shallit, J.
المصدر:
"Example 5.1.7 (The Baum-Sweet Sequence)." Automatic Sequences: Theory, Applications, Generalizations. Cambridge, England: Cambridge University Press
الجزء والصفحة:
...
26-12-2019
1370
Baum-Sweet Sequence
The Baum-Sweet sequence is the sequence of numbers ![<span style=]()
{b_n}" src="http://mathworld.wolfram.com/images/equations/Baum-SweetSequence/Inline1.gif" style="height:15px; width:23px" /> 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."
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