A106826 Trajectory of 1 under the morphism 1->{2,1}, 2->{2,3}, 3->{4,3}, 4->{4,1}.

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

Offset: 0

Author

N. J. A. Sloane, May 20 2005

Keywords

• nonn
• easy

Comments

This is the reverse of the morphism in A105500 and the trajectory of 1 actually starts with 2 instead of 1.

Links

• F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A105500.

Programs

Mathematica

Nest[ Flatten[ # /. {1 -> {2, 1}, 2 -> {2, 3}, 3 -> {4, 3}, 4 -> {4, 1}}] &, {1}, 8] (*Robert G. Wilson v, Jun 20 2005 *)

PARI

{a(n)=local(A);if(n<0, 0, n++; A=[2]; while(length(A)