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A073057 Start with the word 1234, repeatedly append the words obtained via the maps 1 -> 12, 2 -> 13, 3 -> 42, 4 -> 43.

%I A073057 #33 Dec 19 2024 11:46:19
%S A073057 1,2,3,4,1,2,1,3,4,2,4,3,1,2,1,3,4,2,4,3,1,2,1,3,1,2,4,2,4,3,1,3,4,3,
%T A073057 4,2,1,2,1,3,4,2,4,3,1,2,1,3,1,2,4,2,4,3,1,3,4,3,4,2,1,2,1,3,1,2,4,2,
%U A073057 4,3,1,3,4,3,4,2,1,2,1,3,1,2,4,2,1,2,1,3,4,3,1,3,4,3,4,2,1,2,4,2,4,3,4,2,4
%N A073057 Start with the word 1234, repeatedly append the words obtained via the maps 1 -> 12, 2 -> 13, 3 -> 42, 4 -> 43.
%C A073057 Fixed point of the morphism 1 -> 12, 2 -> 13, 3 -> 42, 4 ->43, starting from a(1-4) = 1234. - _Robert G. Wilson v_, Apr 02 2009 [not quite correct, see name, _Joerg Arndt_, Feb 27 2018]
%H A073057 Vincenzo Librandi, <a href="/A073057/b073057.txt">Table of n, a(n) for n = 1..2900</a>
%H A073057 Scott Balchin and Dan Rust, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Rust/rust3.html">Computations for Symbolic Substitutions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
%H A073057 Kevin Ryde, <a href="http://user42.tuxfamily.org/seq-A073057-append-morphism/index.html">PARI/GP Code and Notes</a>.
%e A073057 The first step takes {1,2,3,4} to {1,2,3,4, 1,2, 1,3, 4,2, 4,3}.
%e A073057 The next takes this to {1,2,3,4,1,2,1,3,4,2,4,3, 1,2, 1,3, 4,2, 4,3, 1,2, 1,3, 1,2, 4,2, 4,3, 1,3, 4,3, 4,2}
%t A073057 Nest[ Flatten[ Join[ #, # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> {4, 2}, 4 -> {4, 3}}]] &, {1, 2, 3, 4}, 3] (* _Robert G. Wilson v_, Apr 02 2009 *)
%o A073057 (PARI) \\ See links.
%Y A073057 Cf. A100260 (morphism as 0..3).
%Y A073057 Cf. A020987, A073058.
%K A073057 nonn
%O A073057 1,2
%A A073057 _Roger L. Bagula_, Aug 16 2002
%E A073057 New name using a (corrected) comment by Robert G. Wilson from _Joerg Arndt_, Feb 27 2018