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A276793 Indicator function for A003144. 7


%S 1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,

%T 0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,

%U 1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0

%N Indicator function for A003144.

%C a(n) = 1 iff n is a member of A003144.

%C The binary complement of (a(n)) is called the "binary Tribonacci word" in Mousavi and Shallit (see Theorem 23). It is defined as the change of alphabet {0,1,2} -> {0,1,1} of the Tribonacci word 0102010010... - _Michel Dekking_, Oct 12 2019

%H Michel Dekking, <a href="/A276793/b276793.txt">Table of n, a(n) for n = 1..10000</a>

%H Wolfdieter Lang, <a href="https://arxiv.org/abs/1810.09787">The Tribonacci and ABC Representations of Numbers are Equivalent</a>, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

%H Hamoon Mousavi, Jeffrey Shallit, <a href="https://arxiv.org/abs/1407.5841">Mechanical Proofs of Properties of the Tribonacci Word</a>, arXiv:1407.5841 [cs.FL], 2014.

%H H. Mousavi and J. Shallit, <a href="https://doi.org/10.1007/978-3-319-23660-5_15">Mechanical Proofs of Properties of the Tribonacci Word</a>, In: Manea F., Nowotka D. (eds) Combinatorics on Words. WORDS 2015. Lecture Notes in Computer Science, vol 9304. Springer, 2015, pp. 170-190.

%F a(n) = (A080843(n-1)-1)*(A080843(n-1)-2)/2. - _Wolfdieter Lang_, Dec 06 2018

%Y Cf. A003144, A080843, A276796.

%Y A276793(n)+A276794(n)+A276791(n)=1; A276796(n)+A276797(n)+A276798(n)=n+1.

%K nonn,easy,changed

%O 1

%A _N. J. A. Sloane_, Oct 28 2016

%E Data and offset changed by _Michel Dekking_, Oct 12 2019

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)