

A284948


1limiting 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
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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 0limiting 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



