

A328979


Trajectory of 0 under repeated application of the morphism 0 > 0010, 1 > 1010.


5



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

1


COMMENTS

The morphism in the definition, 0 > 0010, 1 > 1010, is the square of the morphism tau: 0 > 10, 1 > 00.
This sequence is also the 0limiting word of tau (see A284948).
It is also the image of A080426 under the morphism 1 > 0,0,1,0; 3 > 0,0,1,0,1,0,1,0.
This sequence underlies all of A297469, A298468, A328190, and A328196.
Theorem: a(n) = 1 iff the binary expansion of n1 ends in an odd number of 0's (cf. A036554, A072939). For proof see comments by Michel Dekking in A284948.
Is this A096268 with an additional 0 added in front?  R. J. Mathar, Nov 13 2019 [Yes: it follows, e.g., from the above theorem.  Andrey Zabolotskiy, Jan 12 2020]


LINKS

Table of n, a(n) for n=1..85.


MAPLE

F(0):= (0, 0, 1, 0): F(1):= (1, 0, 1, 0):
B:= [0]: # if start at 0 get the present sequence, if start at 1 get A284948
for i from 1 to 4 do B:= map(F, B) od:
B;
# Or, construction via A080426:
f(1):= (1, 3, 1): f(3):= (1, 3, 3, 3, 1):
A:= [1]:
for i from 1 to 5 do A:= map(f, A) od:
A;
g(1):= (0, 0, 1, 0); g(3):= (0, 0, 1, 0, 1, 0, 1, 0);
map(g, A):


MATHEMATICA

SubstitutionSystem[{0 > {0, 0, 1, 0}, 1 > {1, 0, 1, 0}}, 0, 4] // Last (* JeanFrançois Alcover, Apr 06 2020 *)


CROSSREFS

Cf. A036554, A072939, A080426, A284948, A297469, A298468, A328190, A328196.
Sequence in context: A049320 A284817 A309766 * A284524 A226474 A309768
Adjacent sequences: A328976 A328977 A328978 * A328980 A328981 A328982


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Nov 04 2019. Extensively revised Nov 05 2019 thanks to comments from R. J. Mathar.


STATUS

approved



