A308898 Fixed point of the morphism 0 -> 01, 1 -> 2, 2 -> 3, 3 -> 012.

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

Offset: 0

Author

N. J. A. Sloane, Jul 24 2019

Keywords

• nonn

Comments

This is superficially similar to A014587, although the latter sequence is not well understood. - N. J. A. Sloane, Jul 28 2019

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..15126
• M. Dekking, Base phi representations and golden mean beta-expansions, arXiv:1906.08437 [math.NT], June 2019.

Crossrefs

Cf. A014587. See A309198 for another version.

Programs

Mathematica

Nest[Flatten[ReplaceAll[#,{0->{0,1},1->2,2->3,3->{0,1,2}}]]&,{0},10] (* Paolo Xausa, Nov 09 2023 *)

PARI

M = [[1,2], [3], [4], [1,2,3]]; s = [1]; for (k=1, 100, while (k>#s, s=concat(apply(d -> M[d],s))); print1 (s[k]-1 ", ")); \\ Rémy Sigrist, Jul 25 2019