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

1,2

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

Formula

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

Mathematica

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

Prog

(PARI)  {a(n) = my(v = [1]); if( n<1, 0, while( #v<n, v = concat( vector(#v, i, [[1, 2], [2, 3], [3, 1]] [v[i]]))); v[n])}; /* Michael Somos, Aug 05 2014 */

Crossrefs

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

Essentially the same as A071858.

Sequence in context: A350883 A072832 A080328 * A031266 A238459 A109301

Adjacent sequences: A245552 A245553 A245554 * A245556 A245557 A245558

Keyword

nonn

Author

N. J. A. Sloane, Aug 03 2014

Status

approved