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Limiting 0-word of the morphism 0 -> 11, 1 -> 01.
4

%I #11 Oct 01 2024 15:23:21

%S 0,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,

%T 0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,

%U 1,1,0,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1

%N Limiting 0-word of the morphism 0 -> 11, 1 -> 01.

%H Clark Kimberling, <a href="/A285383/b285383.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%F a(n) = A285384(n) for n>=2.

%F Conjecture: a(n) = A035263(n-1). - _R. J. Mathar_, May 08 2017

%e 0 -> 11-> 0101 -> 11011101 -> 0101110101011101 ->

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1}}] &, {0}, 10] (* A285383 *)

%t Flatten[Position[s, 0]] (* A171947 *)

%t Flatten[Position[s, 1]] (* A171946 *)

%t SubstitutionSystem[{0->{1,1},1->{0,1}},{0,1},{6}][[1]] (* _Harvey P. Dale_, Oct 01 2024 *)

%Y Cf. A171947, 171946, A285384.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 26 2017