A317953 Apply the morphism 1 -> {1, 2}, 2 -> {3,1}, 3 -> {1} n times to 1, and concatenate the resulting string.

1, 12, 1231, 1231112, 1231112121231, 123111212123112311231112, 12311121212311231123111212311121231112121231, 123111212123112311231112123111212311121212311231112121231123111212123112311231112

Offset: 1

Author

N. J. A. Sloane, Aug 21 2018

Keywords

• nonn

Comments

For the tribonacci word A092782, each block b(n) (see A103269) is the concatenation of the three previous blocks: b(n) = b(n-1).b(n-2).b(n-3). Instead, here we have a(n) = a(n-1).a(n-3).a(n-2), as can be seen in the examples section below.

Examples

			a(1): 1,
a(2): 12,
a(3): 1231,
a(4): 1231112,
a(5): 1231112121231,
a(6): 123111212123112311231112,
a(7): 12311121212311231123111212311121231112121231,
equals a(6).a(4).a(5), look:
a(6):123111212123112311231112,
a(4):                        1231112,
a(5):                               1231112121231,
a(8): 123111212123112311231112123111212311121212311231112121231123111212123112311231112
equals a(7).a(5).a(6), look:
a(7): 12311121212311231123111212311121231112121231,
a(5):                                             1231112121231,
a(6):                                                          123111212123112311231112,
		

References

• V. F. Sirvent, Semigroups and the self-similar structure of the flipped tribonacci substitution, Applied Math. Letters, 12 (1999), 25-29.

Crossrefs

Cf. A100619 (the limiting string), A277735, A317953.

A103269 is the analog for the word A092782.