A073058 Define s(1)={1,2}, s(2)={1,3} and s(3)={1}. For a finite sequence A={a_1, ..., a_n}, with elements in {1,2,3}, define t(A) to be the concatenation of A, s(a_1), s(a_2), ... and s(a_n). Start with the sequence {1,2,3} and repeatedly apply t; limiting sequence is shown.

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

Offset

1,2

Comments

A fractal sequence related to a sequence of Rauzy.

Links

Table of n, a(n) for n=1..105.

P. Arnoux and E. Harriss, What is a Rauzy Fractal?, Notices Amer. Math. Soc., 61 (No. 7, 2014), 768-770, also p. 704 and front cover.

Vincent Canterini and Anne Siegel, Geometric Representations of Substitutions of Pisot Type, Trans. Amer. Math. Soc. 353 (2001), 5121-5144.

Mathematica

Nest[ Flatten[ Join[#, # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}}]] &, {1, 2, 3},
4] (* Robert G. Wilson v, Jan 01 2017 *)

Crossrefs

Cf. A092782, A103684, A105083, A245553, A245554.

Sequence in context: A190496 A193926 A211450 * A100336 A275609 A006376

Adjacent sequences: A073055 A073056 A073057 * A073059 A073060 A073061

Keyword

nonn

Author

Roger L. Bagula, Aug 16 2002

Status

approved