A275855 - OEIS

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A275855

Platinum mean sequence: fixed point of the morphism 0 -> 0001, 1 -> 001.

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

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OFFSET

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

Table of n, a(n) for n=1..112.

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

Adjacent sequences: A275852 A275853 A275854 * A275856 A275857 A275858

KEYWORD

nonn

AUTHOR

Dan Rust, Aug 11 2016

STATUS

approved