A100260 Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 31, 3 -> 32.

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

Offset

1,4

Comments

This is a version of the Rudin-Shapiro sequence A020987. - N. J. A. Sloane, Jan 17 2021

References

Dekking, Michel, Michel Mendes France, and Alf van der Poorten. "Folds." The Mathematical Intelligencer, 4.3 (1982): 130-138 & front cover, and 4:4 (1982): 173-181 (printed in two parts).

Lipshitz, Leonard, and A. van der Poorten. "Rational functions, diagonals, automata and arithmetic." In Number Theory, Richard A. Mollin, ed., Walter de Gruyter, Berlin (1990): 339-358.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..16384

Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.

James D. Currie, Narad Rampersad, Kalle Saari, Luca Q. Zamboni, Extremal words in morphic subshifts, Discrete Math. 322 (2014), 53--60. MR3164037. See Sect. 8.

L. Lipshitz and A. J. van der Poorten, Rational functions, diagonals, automata and arithmetic

Rémy Sigrist, Colored scatterplot of (n, 4*b(n) - n) for n = 1..2^20 (where b is the ordinal transform of the sequence)

Index entries for sequences that are fixed points of mappings

Mathematica

Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {0, 2}, 2 -> {3, 1}, 3 -> {3, 2}})]}], {0}, 7] (* Robert G. Wilson v, Feb 28 2005 *)

Crossrefs

Cf. A073057, A020987.

Sequence in context: A178107 A272472 A355536 * A165317 A174067 A124943

Adjacent sequences: A100257 A100258 A100259 * A100261 A100262 A100263

Keyword

nonn

Author

Ralf Stephan, Nov 18 2004

Extensions

More terms from Robert G. Wilson v, Nov 20 2004

Status

approved