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Fixed point of the morphism 0->11, 1-> 110.
5

%I #11 Nov 30 2023 15:12:36

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

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

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

%N Fixed point of the morphism 0->11, 1-> 110.

%H Clark Kimberling, <a href="/A285431/b285431.txt">Table of n, a(n) for n = 1..10000</a>

%H J. Shallit, <a href="https://arxiv.org/abs/2310.14252">Proof of Irvine's conjecture via mechanized guessing</a>, arXiv preprint arXiv:2310.14252 [math.CO], October 22 2023.

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

%e 0 -> 11 -> 110110- -> 1101101111011011 -> 11011011110110111101101101101111011011110110 ->

%t s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {1, 1, 0}}] &, {0}, 13] (* A285431 *)

%t Flatten[Position[s, 0]] (* A026368 *)

%t Flatten[Position[s, 1]] (* A026367 *)

%o (Python)

%o from itertools import islice

%o def A285431_gen(): # generator of terms

%o a, l = [1,1], 0

%o while True:

%o yield from a[l:]

%o c = sum(([1,1,0] if d else [1,1] for d in a),start=[])

%o l, a = len(a), c

%o A285431_list = list(islice(A285431_gen(),30)) # _Chai Wah Wu_, Nov 30 2023

%Y Cf. A026367, A026368.

%K nonn,easy

%O 1

%A _Clark Kimberling_, Apr 29 2017