A100619 Fixed point of the morphism 1 -> 12, 2 -> 31, 3 -> 1, starting from a(1) = 1.

1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2

Offset: 1

Author

N. J. A. Sloane, Dec 03 2004

Keywords

• nonn
• easy

Comments

Sirvent comments that in spite of the similarity of this map to the one in A092782, the two sequences have very different properties. They have different complexities, different Rauzy fractals, etc.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
• Victor F. Sirvent, Semigroups and the self-similar structure of the flipped tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29.
• Victor F. Sirvent, The common dynamics of the Tribonacci substitutions, Bulletin of the Belgian Mathematical Society-Simon Stevin 7.4 (2000): 571-582.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A092782.

Programs

Maple

f(1):= (1, 2): f(2):= (3, 1): f(3):= (1): B:= [1]:
for i from 1 to 12 do B:= map(f, B) od:
B; # N. J. A. Sloane, Aug 17 2018

Mathematica

Nest[ Function[l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {3, 1}, 3 -> {1}})]}], {1}, 7][[1]] (* Robert G. Wilson v, Feb 26 2005 *)

Extensions

More terms from Robert G. Wilson v, Dec 05 2004