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A269927
Start with A_0 = 0, then extend by setting B_k = complement of A_k and A_{k+1} = A_k C_1 C_2 ... C_m, where m is the length of A_k and C_i = A_k if the i-th element of A_k is 1 and C_i = B_k otherwise; sequence is limit of A_k as k -> infinity.
1
0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1
OFFSET
0
COMMENTS
Similar to the Thue-Morse sequence, with the replication rule determined by the bits in A_k at each step.
The lengths of A_i's are 1, 2, 6, 42, 1806,... (A007018).
EXAMPLE
The first few A_k are:
A_0 = 0
A_1 = 0,1
A_2 = 0,1,1,0,0,1
A_3 = 0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1
PROG
(Python)
A269927_list = [0]
for _ in range(5):
ylist = [1-d for d in A269927_list]
zlist = list(A269927_list)
for i in A269927_list:
if i:
zlist += A269927_list
else:
zlist += ylist
A269927_list = zlist
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane and Chai Wah Wu, Mar 08 2016
STATUS
approved