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A143667 Digits of the infinite Fibonacci word A003849 grouped 2 by 2 and interpreted as a binary value. 4
1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Group 2 by 2 the successive letters of the infinite Fibonacci word A003849 then apply: 00->0, 01->1 and 10->2.

Also result of the following iterated morphism: 1->1022, 0->10221, 2->1021, iterated from letter 1. (Monnerot 2008)

Fractal properties studied (proposed for publication)

(a(n)) is essentially the same sequence as A123564. Simply change the alphabet to {1,2,3}, and permute the letters. The Standard Form of (a(n)) written as a word on the alphabet {a,b,c} is abccabccaabc... . Other forms for this standard form are 1,2,3,3,1,2,3,3,1,1,2,3,.... and 123312331123... - _Michel Dekking, Oct 07 2017

(a(n)) is the fixed point of the 2-block map (called 2-block Fibonacci to the power 3) 00->0100101001, 01->01001010, 10->01001001, followed by the coding above. - Michel Dekking, Sep 26 2017

REFERENCES

M. Lothaire, Combinatorics on words, Cambridge University Press.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

J.-P. Allouche, M. Mendès France, and G. Skordev, Non-intersectivity of Paperfolding Dragon Curves and of Curves Generated by Automatic Sequences, INTEGERS, Electronic Journal of Combinatorial Number Theory, vol. 18A, Article #A2, 2018. Mentions this sequence.

F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.

A. Monnerot-Dumaine, Fibonacci Fractal

A. Monnerot-Dumaine, The Fibonacci Word Fractal [From Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Aug 31 2009]

J. L. Ramírez, G. N. Rubiano, Properties and Generalizations of the Fibonacci Word Fractal, The Mathematica Journal, Vol. 16 (2014). See "Dense Fibonacci word". - N. J. A. Sloane, Mar 26 2014

FORMULA

a(n) = decimal value of b(2n-1)b(2n), b(n) taken from A003849 (infinite Fibonacci word).

EXAMPLE

a(1) = 1 because the infinite Fibonacci word starts with "01", a(2) = 0 because it continues with "00", and so on.

MATHEMATICA

Table[3 - (Floor[#1 #2] - 2 Floor[#1 (#2 - 1)] + Floor[#1 (#2 + 1)]) & @@ {1/GoldenRatio, 2 n}, {n, 100}] (* Michael De Vlieger, Oct 06 2017 *)

PROG

(Haskell)

a143667 n = a143667_list !! (n-1)

a143667_list = f a003849_list where

   f (0:0:ws) = 0 : f ws; f (0:1:ws) = 1 : f ws; f (1:0:ws) = 2 : f ws

-- Reinhard Zumkeller, Jul 29 2014

CROSSREFS

Cf. A003849, A123564.

Sequence in context: A282947 A287200 A284387 * A299485 A246785 A084934

Adjacent sequences:  A143664 A143665 A143666 * A143668 A143669 A143670

KEYWORD

easy,nonn,word

AUTHOR

Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Aug 28 2008

STATUS

approved

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Last modified October 23 06:23 EDT 2018. Contains 316520 sequences. (Running on oeis4.)