

A269723


Start with A_0 = 0, then extend by setting B_k = complement of A_k and A_{k+1} = A_k A_k B_k B_k; sequence is limit of A_k as k > infinity.


3



0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1
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OFFSET

0


COMMENTS

Equivalently, trajectory of 0 under the morphism 0 > 0011, 1 > 1100.
a(n) is the number of 1's, mod 2, in the 2^{odd} positions of the binary representation of n.  Jon Hart, Aug 09 2016


LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..16383
Index entries for sequences that are fixed points of mappings


EXAMPLE

The first few A_k are:
A_0 = 0,
A_1 = 0,0,1,1,
A_2 = 0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,
A_3 = 0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,
...


MATHEMATICA

Table[Mod[#, 2] &@ Count[Drop[#, {1, Length@ #, 2}], 1] &@ Reverse@ IntegerDigits[n, 2], {n, 120}] (* Michael De Vlieger, Aug 11 2016 *)


PROG

(Python)
A269723_list = [0]
for _ in range(7):
A269723_list += A269723_list + [1d for d in A269723_list]*2 # Chai Wah Wu, Mar 04 2016
(Python)
A269723_list = [bin(_&0xaaaaa).count('1')%2 for _ in range(16384)] # Jon Hart, Aug 09 2016


CROSSREFS

The ThueMorse A010060 and A189718 have similar definitions.
Sequence in context: A285501 A288551 A327174 * A284487 A156660 A155899
Adjacent sequences: A269720 A269721 A269722 * A269724 A269725 A269726


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 04 2016. Thanks to Chai Wah Wu for correcting an error in my initial submission.


STATUS

approved



