A316831 Trajectory of 0 under repeated application of the morphism 0 -> 01, 1 -> 21, 2 -> 13, 3 -> 33.

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

Offset: 0

Author

N. J. A. Sloane, Jul 18 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000
• A. Cobham, On the Hartmanis-Stearns problem for a class of tag machines, 9th Annual Symposium on Switching and Automata Theory (SWAT 1968)(FOCS), pp. 51-60, 1968; doi:10.1109/SWAT.1968.20. See Example 7.

Crossrefs

Cf. A086747, A316832.

Programs

Maple

f(0):= (0,1):
f(1):= (2,1):
f(2):= (1,3):
f(3):= (3,3):
A:= [0]:
for i from 1 to 8 do A:= map(f, A) od:
A; # Robert Israel, Jul 18 2018

Mathematica

Nest[ Flatten[# /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {1, 3}, 3 -> {3, 3}}] &, {0}, 7] (* Robert G. Wilson v, Jul 18 2018 *)