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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 18 2017
STATUS
approved