A005681 A squarefree quaternary sequence.

2, 4, 3, 2, 3, 1, 2, 4, 3, 1, 2, 3, 2, 4, 3, 2, 3, 1, 2, 3, 2, 4, 3, 1, 2, 4, 3, 2, 3, 1, 2, 4, 3, 1, 2, 3, 2, 4, 3, 1, 2, 4, 3, 2, 3, 1, 2, 3, 2, 4, 3, 2, 3, 1, 2, 4, 3, 1, 2, 3, 2, 4, 3, 2, 3, 1, 2, 3, 2, 4, 3, 1, 2, 4, 3, 2, 3, 1, 2, 3, 2, 4, 3, 2, 3, 1, 2, 4, 3, 1, 2, 3, 2, 4, 3, 1, 2, 4, 3, 2, 3, 1, 2, 4, 3, 1, 2, 3, 2, 4, 3, 2, 3, 1, 2

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This is an automatic sequence, fixed point starting with 2 of the morphism mu: 1->23, 2->24, 3->31, 4->32. The morphism mu is the 2-block morphism of the Thue-Morse morphism. An instance of this sequence on the alphabet {0,1,2,3} is equal to A245188. - Michel Dekking, Feb 18 2021

References

• A. Salomaa, Jewels of Formal Language Theory. Computer Science Press, Rockville, MD, 1981, p. 10.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..10000
• F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
• G. Siebert, Letter to N. J. A. Sloane, Sept. 1977

Crossrefs

Cf. A001285, A005679, A245188.

Formula

a(n) = s(A001285(n), A001285(n+1)) where s(1,1)=1, s(1,2)=2, s(2,1)=3, s(2,2)=4. - Sean A. Irvine, Aug 04 2016