A317952 Trajectory of 1 under repeated application of the morphism 1->121, 2->232, 3->343, 4->414.

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

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Julien Cassaigne, Juhani Karhumäki, Svetlana Puzynina, On k-abelian palindromes, Information and Computation, Volume 260, June 2018, Pages 89-98. See Lemma 1.

Formula

From Robert Israel, Aug 20 2018: (Start)

a(3*k) = a(3*k+2) = a(k).

a(3*k+1) == 1 + a(k) mod 4. (End)

Maple

A:= [1]:
for k from 1 to 5 do A:= subs([1=(1, 2, 1), 2=(2, 3, 2), 3=(3, 4, 3), 4=(4, 1, 4)], A);
od:
op(A); # Robert Israel, Aug 20 2018

Mathematica

SubstitutionSystem[{1 -> {1, 2, 1}, 2 -> {2, 3, 2}, 3 -> {3, 4, 3}, 4 -> {4, 1, 4}}, 1, 5] // Last (* Jean-François Alcover, Apr 06 2020 *)

Crossrefs

Sequence in context: A286281 A229830 A105203 * A059131 A059129 A349954

Adjacent sequences: A317949 A317950 A317951 * A317953 A317954 A317955

Keyword

nonn

Author

N. J. A. Sloane, Aug 20 2018

Status

approved