A100260 - OEIS

%I #36 Aug 06 2024 06:42:20

%S 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,

%T 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,

%U 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

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

%C This is a version of the Rudin-Shapiro sequence A020987. - _N. J. A. Sloane_, Jan 17 2021

%D 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).

%D 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.

%H Rémy Sigrist, <a href="/A100260/b100260.txt">Table of n, a(n) for n = 1..16384</a>

%H Scott Balchin and Dan Rust, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Rust/rust3.html">Computations for Symbolic Substitutions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.

%H James D. Currie, Narad Rampersad, Kalle Saari, Luca Q. Zamboni, <a href="http://dx.doi.org/10.1016/j.disc.2014.01.002">Extremal words in morphic subshifts</a>, Discrete Math. 322 (2014), 53--60. MR3164037. See Sect. 8.

%H L. Lipshitz and A. J. van der Poorten, <a href="https://citeseerx.ist.psu.edu/pdf/dfa9976c3141d5a40b1cf14231cbcbc85504b61e">Rational functions, diagonals, automata and arithmetic</a>

%H Rémy Sigrist, <a href="/A100260/a100260.png">Colored scatterplot of (n, 4*b(n) - n) for n = 1..2^20</a> (where b is the ordinal transform of the sequence)

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

%t 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 *)

%Y Cf. A073057, A020987.

%K nonn

%O 1,4

%A _Ralf Stephan_, Nov 18 2004

%E More terms from _Robert G. Wilson v_, Nov 20 2004