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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 + [1-d 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 Thue-Morse 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

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Last modified May 7 17:52 EDT 2021. Contains 343652 sequences. (Running on oeis4.)