A245555 Trajectory of 1 under the morphism 1 -> 12, 2 -> 23, 3 -> 31.

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

Offset: 1

Author

N. J. A. Sloane, Aug 03 2014

Keywords

• nonn

Comments

The morphism 1->12, 2->21 gives the {1,2} version of the Thue-Morse sequence A001285, cf. A010060.

The morphism 0->01, 1->12, 2->20 gives the generalized Thue-Morse sequence A071858.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are fixed points of mappings

Crossrefs

Cf. A001285, A010060, A092782, A105083, A245553, A245554.

Essentially the same as A071858.

Programs

Mathematica

Nest[ Function[ l, {Flatten[(l /. {1 -> {1, 2}, 2 -> {2, 3}, 3 -> {3, 1}})] }], {1}, 9]

PARI

{a(n) = my(v = [1]); if( n<1, 0, while( #vMichael Somos, Aug 05 2014 */

Formula

a(n) = A071858(n+1) + 1. - Michel Dekking, Sep 29 2020