login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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 0-limiting 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 n-1 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

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):

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)