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

Author

Ralf Stephan, Nov 18 2004

Keywords

• nonn

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

Crossrefs

Cf. A073057, A020987.

Programs

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 *)

Extensions

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