

A317948


An example of a morphic word: the sorted (by length, then alphabetically) sequence of words of the form a*b* under the action of a finite automaton defined as follows: start state is 0; a and b map states [0, 1, 2, 3] to states [1, 2, 3, 0] and [0, 3, 1, 2], respectively.


1



0, 1, 0, 2, 3, 0, 3, 1, 2, 0, 0, 2, 3, 1, 0, 1, 0, 1, 2, 3, 0, 2, 3, 0, 3, 1, 2, 0, 3, 1, 2, 0, 2, 3, 1, 0, 0, 2, 3, 1, 0, 1, 2, 3, 0, 1, 0, 1, 2, 3, 0, 3, 1, 2, 0, 2, 3, 0, 3, 1, 2, 0, 2, 3, 1, 0, 3, 1, 2, 0, 2, 3, 1, 0, 1, 2, 3, 0, 0, 2, 3, 1, 0, 1, 2, 3, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

The DuchĂȘne et al. (2011) reference mentions many other sequences that are of great interest.


REFERENCES

Rigo, Michel, and Arnaud Maes. "More on generalized automatic sequences." Journal of Automata, Languages and Combinatorics 7.3 (2002): 351376. See Fig. 3.


LINKS

Table of n, a(n) for n=1..87.
Eric DuchĂȘne, Aviezri S. Fraenkel, Richard J. Nowakowski, and Michel Rigo, Extensions and restrictions of Wythoff's game preserving Wythoff's sequence as set of Ppositions, Slides from a talk, LIAFA, Paris, October 21, 2011. See around the 35th slide, a slide with first line "In fact, this is a special case of the following result...".
Michel Rigo, Generalization of automatic sequences for numeration systems on a regular language, Theoret. Comput. Sci., 244 (2000) 271281.


PROG

(Python)
aut0, aut1 = [1, 2, 3, 0], [0, 3, 1, 2]
a, row = [0], [0]
for i in range(1, 10):
row = [aut0[row[0]]] + [aut1[x] for x in row]
a += row
print(a)
# Andrey Zabolotskiy, Aug 17 2018


CROSSREFS

Sequence in context: A132385 A191716 A089235 * A334291 A051910 A137998
Adjacent sequences: A317945 A317946 A317947 * A317949 A317950 A317951


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Aug 12 2018


EXTENSIONS

New name and terms a(51) and beyond from Andrey Zabolotskiy, Aug 17 2018


STATUS

approved



