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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

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OFFSET

0,3

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.

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 *)

CROSSREFS

Cf. A086747, A316832.