

A270788


Unique fixed point of the 3symbol Fibonacci morphism phihat_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
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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



