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A316826 Image of 3 under repeated application of the morphism 3 -> 3,2, 2 -> 1,0,2,0,1,2, 1 -> 1,0,1,2, 0 -> 0,2.

%I A316826 #19 Jul 30 2020 14:00:16
%S A316826 3,2,1,0,2,0,1,2,1,0,1,2,0,2,1,0,2,0,1,2,0,2,1,0,1,2,1,0,2,0,1,2,1,0,
%T A316826 1,2,0,2,1,0,1,2,1,0,2,0,1,2,0,2,1,0,2,0,1,2,1,0,1,2,0,2,1,0,2,0,1,2,
%U A316826 0,2,1,0,1,2,1,0,2,0,1,2,0,2,1,0,2,0,1,2,1,0,1,2,0,2,1,0,1,2,1,0
%N A316826 Image of 3 under repeated application of the morphism 3 -> 3,2, 2 -> 1,0,2,0,1,2, 1 -> 1,0,1,2, 0 -> 0,2.
%C A316826 A word that is pure morphic and uniform morphic, but neither pure uniform morphic, nor primitive morphic, nor recurrent.
%H A316826 Robert Israel, <a href="/A316826/b316826.txt">Table of n, a(n) for n = 0..10000</a>
%H A316826 Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, <a href="https://arxiv.org/abs/1711.10807">A Taxonomy of Morphic Sequences</a>, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.
%p A316826 S:= [3=(3,2), 2 = (1,0,2,0,1,2), 1 = (1,0,1,2), 0 = (0,2)]:
%p A316826 A:= [3]:
%p A316826 for iter from 1 do
%p A316826   Ap:= subs(S,A);
%p A316826   if nops(Ap) > 100 then Ap:= Ap[1..100] fi;
%p A316826   if Ap = A then break fi;
%p A316826   A:= Ap
%p A316826 od:
%p A316826 A; # _Robert Israel_, Jul 30 2020
%t A316826 SubstitutionSystem[{3 -> {3, 2}, 2 -> {1, 0, 2, 0, 1, 2}, 1 -> {1, 0, 1, 2}, 0 -> {0, 2}}, {3}, 4] // Last (* _Jean-François Alcover_, Nov 11 2018 *)
%Y A316826 Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.
%Y A316826 Cf. A036577.
%K A316826 nonn
%O A316826 0,1
%A A316826 _N. J. A. Sloane_, Jul 14 2018