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

Offset: 0

Author

N. J. A. Sloane, Jul 14 2018

Keywords

• nonn

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.

Crossrefs

Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.

Cf. A036577.

Programs

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 *)