A005681 A squarefree quaternary sequence. (Formerly M0934)

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

1,1

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

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

Crossrefs

Cf. A001285, A005679, A245188.

Sequence in context: A064134 A238847 A011030 * A049848 A152026 A345928

Adjacent sequences: A005678 A005679 A005680 * A005682 A005683 A005684

Keyword

nonn

Author

N. J. A. Sloane

Status

approved