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

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, 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, 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

Offset: 1

Author

Roger L. Bagula, Aug 16 2002

Keywords

• nonn

Comments

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]

Examples

			The first step takes {1,2,3,4} to {1,2,3,4, 1,2, 1,3, 4,2, 4,3}.
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}
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2900
• Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
• Kevin Ryde, PARI/GP Code and Notes.

Crossrefs

Cf. A100260 (morphism as 0..3).

Cf. A020987, A073058.

Programs

Mathematica

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 *)

PARI

\\ See links.

Extensions

New name using a (corrected) comment by Robert G. Wilson from Joerg Arndt, Feb 27 2018