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A284948 1-limiting word of the morphism 0 -> 10, 1 -> 00 4
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, 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, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Consider iterations of the morphism defined by 0 -> 10, 1 -> 00: 0 -> 10 -> 0010 -> 10100010 -> 0010001010100010 -> ...  There are two limiting words, one of which has initial term 1 and the other, 0. These are fixed points of the morphism squared: 0-> 0010, 1->1010. [Corrected by Michel Dekking, Jan 06 2019]

The 0-limiting word is 0,0,1,0,0,0,1,0,1,0,1,0,0,0,1,0,... (A328979). It is the characteristic sequence of those natural numbers whose binary representation ends in an odd numbers of zeros, sequence A036554, but with offset 0 (easy to see from the fact that if the binary representation of N is equal to w, then the binary representations of 4N, 4N+1, 4N+2 and 4N+3 are w00, w01, w10 and w11). - Michel Dekking, Jan 06 2019

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

MAPLE

f(0):= (0, 0, 1, 0): f(1):= (1, 0, 1, 0):

A:= [0]: # if start at 0 get A328979, if start at 1 get the present sequence

for i from 1 to 8 do A:= map(f, A) od:

A; # N. J. A. Sloane, Nov 05 2019

MATHEMATICA

s = Nest[Flatten[# /. {0 -> {1, 0}, 1 -> {0, 0}}] &, {0}, 7] (* A284948 *)

u = Flatten[Position[s, 0]]  (* A171946  *)

v = Flatten[Position[s, 1]]  (* A171947 *)

CROSSREFS

Cf. A036554, A171946, A171947, A328979.

Sequence in context: A285142 A267525 A014429 * A011637 A016229 A015869

Adjacent sequences:  A284945 A284946 A284947 * A284949 A284950 A284951

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling, Apr 18 2017

STATUS

approved

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Last modified November 15 21:37 EST 2019. Contains 329168 sequences. (Running on oeis4.)