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A123740 Characteristic sequence for Wythoff AB-numbers A003623. 8
0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Left shifted sequence is the characteristic function of A035336, and also the second lowest digit of the Zeckendorf expansion of n. - Franklin T. Adams-Watters, Jun 30 2009

a(n) = A188009(n+2), n>=1. - Wolfdieter Lang, Jun 27 2011

Doubling the 0’s in the infinite Fibonacci word A003849 gives (a(n)). - Michel Dekking, Sep 09 2016

This is a morphic sequence, i.e., the letter-to-letter image of the fixed point of a morphism. The fixed point is the unique fixed point A270788 of the three symbol Fibonacci morphism. The letter-to-letter map is 1->0, 2->0, 3->1. - Michel Dekking, May 02 2019

REFERENCES

See references under A000201.

LINKS

Table of n, a(n) for n=1..100.

Michel Dekking and Michael Keane, On the conjugacy class of the Fibonacci dynamical system, arXiv preprint arXiv:1608.04487 [math.DS], 2016.

Michel Dekking and Michael Keane, On the conjugacy class of the Fibonacci dynamical system, Theoretical Computer Science 668 (2017), 59-69.

FORMULA

a(n) = 1 if n=A(B(k)) for some k>=1, else 0, with A(k):=A000201(k) and B(k):=A001950(k), k>=1.

a(n) = 1-(1-h(n))-(1-h(n+1)) = h(n)-(1-h(n+1))= h(n)*h(n+1) with h(n):=A005614(n-1), n>=1, the rabbit sequence.

a(n) = A(n+2)-A(n)-3. - Wolfdieter Lang, Jun 27 2011

CROSSREFS

Cf. A003623, A000201, A001950, A188009, A270788.

Cf. A003849, A014417. - Franklin T. Adams-Watters, Jun 30 2009

Sequence in context: A147873 A103589 A305388 * A188472 A286044 A129272

Adjacent sequences:  A123737 A123738 A123739 * A123741 A123742 A123743

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Oct 13 2006

STATUS

approved

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Last modified August 9 13:57 EDT 2020. Contains 336323 sequences. (Running on oeis4.)