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.

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).

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

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

Cf. A010060, A189718, A269723.

Sequence in context: A057215 A284905 A291197 * A374468 A246146 A191162

Adjacent sequences: A269924 A269925 A269926 * A269928 A269929 A269930

Keyword

nonn

Author

N. J. A. Sloane and Chai Wah Wu, Mar 08 2016

Status

approved