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A270788 Unique fixed point of the 3-symbol Fibonacci morphism phi-hat_2. 12
1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 1, 2, 3, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Fixed point of the morphism 1 --> 12, 2 --> 3, 3 --> 12. [Joerg Arndt, Apr 10 2016]

LINKS

Joerg Arndt, Table of n, a(n) for n = 1..1000

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

FORMULA

Let A(n)=floor(n*tau), B(n)=n+floor(n*tau), i.e., A and B are the lower and upper Wythoff sequences, A=A000201, B=A001950. Then a(n)=1 if n=A(A(k)) for some k; a(n)=2 if n=B(k) for some k; a(n)=3 if n=A(B(k)) for some k. - Michel Dekking, Dec 27 2016

MAPLE

with(ListTools);

psi:=proc(S)

Flatten(subs( {1=[1, 2], 2=[3], 3=[1, 2]}, S));

end;

S:=[1];

for n from 1 to 10 do S:=psi(S): od:

S;

CROSSREFS

Cf. A159917 (same sequence if we map 1->2, 2->0, 3->1).

Sequence in context: A295561 A076423 A075660 * A190496 A193926 A211450

Adjacent sequences:  A270785 A270786 A270787 * A270789 A270790 A270791

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 30 2016

EXTENSIONS

More terms from Joerg Arndt, Apr 10 2016

Offset changed to 1 by Michel Dekking, Dec 27 2016

STATUS

approved

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Last modified December 13 12:44 EST 2019. Contains 329968 sequences. (Running on oeis4.)