A316826 - OEIS

A316826

Image of 3 under repeated application of the morphism 3 -> 3,2, 2 -> 1,0,2,0,1,2, 1 -> 1,0,1,2, 0 -> 0,2.

3, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0

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OFFSET

0,1

COMMENTS

A word that is pure morphic and uniform morphic, but neither pure uniform morphic, nor primitive morphic, nor recurrent.

LINKS

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

Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807 [cs.FL], Nov 29 2017.

MAPLE

S:= [3=(3, 2), 2 = (1, 0, 2, 0, 1, 2), 1 = (1, 0, 1, 2), 0 = (0, 2)]:

A:= [3]:

for iter from 1 do

Ap:= subs(S, A);

if nops(Ap) > 100 then Ap:= Ap[1..100] fi;

if Ap = A then break fi;

A:= Ap

od:

A; # Robert Israel, Jul 30 2020

MATHEMATICA

SubstitutionSystem[{3 -> {3, 2}, 2 -> {1, 0, 2, 0, 1, 2}, 1 -> {1, 0, 1, 2}, 0 -> {0, 2}}, {3}, 4] // Last (* Jean-François Alcover, Nov 11 2018 *)