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A120614 a(n)=g(n)-g(n-1) where g(k)=floor(phi*floor(k/phi)) and phi=(1+sqrt(5))/2. 2
0, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

a(floor(k*phi)+k+1)=0 ; a(floor(k*phi)+k+2)=2, if n is not in {floor(k*phi)+k+1}U{floor(k*phi)+k+2}_{k>=1} a(n)=1.

The word obtained after deleting the initial string {0,1}, 0210202102102021020..., is a fixed point of the morphism 02-->10202 and 102-->10210202

MATHEMATICA

#[[2]]-#[[1]]&/@Partition[Table[Floor[GoldenRatio*Floor[n/GoldenRatio]], {n, 0, 110}], 2, 1] (* Harvey P. Dale, Dec 14 2012 *)

CROSSREFS

Cf. A120613, A120615.

Sequence in context: A194313 A127476 A140397 * A287516 A252055 A097567

Adjacent sequences:  A120611 A120612 A120613 * A120615 A120616 A120617

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 17 2006

STATUS

approved

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Last modified August 23 04:06 EDT 2017. Contains 290958 sequences.