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A275855 Platinum mean sequence: fixed point of the morphism 0 -> 0001, 1 -> 001. 3
0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
The morphism has expansion factor P = 2 + sqrt(3) - the platinum mean. That is, on average the length of the n-th iterate of the morphism on a word w of length |w| is |w|P^n.
(a(n)) is a Sturmian word (floor(n*alpha) - floor((n-1)*alpha)) for alpha = 2-sqrt(3). Cf. A188068. - Michel Dekking, Feb 07 2017
REFERENCES
M. Baake and U. Grimm, Aperiodic Order. Vol. 1: A Mathematical Invitation, Cambridge University Press, Cambridge, 2013, pages 93-94.
LINKS
Scott Balchin and Dan Rust, Computations for Symbolic Substitutions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.1.
EXAMPLE
0->0001->000100010001001->->
MATHEMATICA
{0}~Join~Rest@ Flatten@ SubstitutionSystem[{0 -> {0, 0, 0, 1}, 1 -> {0, 0, 1}}, {1}, 4] (* Version 10.2, or *)
Nest[Flatten[# /. {0 -> {0, 0, 0, 1}, 1 -> {0, 0, 1}}] &, {1}, 4] (* Michael De Vlieger, Aug 15 2016, latter after Robert G. Wilson v at A096268 *)
CROSSREFS
Cf. A019973 (2 + sqrt(3)), A276865.
Sequence in context: A331282 A331169 A144602 * A268310 A283316 A284508
KEYWORD
nonn
AUTHOR
Dan Rust, Aug 11 2016
STATUS
approved

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Last modified May 18 08:32 EDT 2024. Contains 372618 sequences. (Running on oeis4.)