A316340 Image of 1 under repeated application of the morphism 1 -> 12312, 2 -> 341, 3 -> 34134, 4 -> 123,

1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 3, 4, 1, 2, 3, 1, 2

Offset

0,2

Comments

Following this with the morphism 1,2 -> 0, 3,4 -> 1 gives A275129.

Links

Table of n, a(n) for n=0..98.

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.

Mathematica

SubstitutionSystem[{1 -> {1, 2, 3, 1, 2}, 2 -> {3, 4, 1}, 3 -> {3, 4, 1, 3, 4}, 4 -> {1, 2, 3}}, {1}, 4] // Last (* Jean-François Alcover, Aug 05 2018 *)

Crossrefs

Cf. A275129.

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.

Sequence in context: A194063 A194053 A194050 * A002828 A191091 A098066

Adjacent sequences: A316337 A316338 A316339 * A316341 A316342 A316343

Keyword

nonn

Author

N. J. A. Sloane, Jul 14 2018

Status

approved