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A269723
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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.
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5
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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)
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OFFSET
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0
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COMMENTS
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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
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LINKS
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EXAMPLE
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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,
...
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MATHEMATICA
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Table[Mod[#, 2] &@ Count[Drop[#, {1, Length@ #, 2}], 1] &@ Reverse@ IntegerDigits[n, 2], {n, 120}] (* Michael De Vlieger, Aug 11 2016 *)
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PROG
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(Python)
for _ in range(7):
(Python)
A269723_list = [bin(_&0xaaaaa).count('1')%2 for _ in range(16384)] # Jon Hart, Aug 09 2016
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CROSSREFS
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A355340 gives a perspective of the relationship to Thue-Morse.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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