A276793 Indicator function for A003144.

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, 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, 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

Offset

1

Comments

a(n) = 1 iff n is a term of A003144.

The binary complement of (a(n)) is called the "binary Tribonacci word" in Mousavi and Shallit (see Theorem 23). It is defined to be the change of alphabet {0,1,2} -> {0,1,1} of the tribonacci word 0102010010... - Michel Dekking, Oct 12 2019

Links

Michel Dekking, Table of n, a(n) for n = 1..10000

Wolfdieter Lang, The Tribonacci and ABC Representations of Numbers are Equivalent, arXiv preprint arXiv:1810.09787 [math.NT], 2018.

Hamoon Mousavi and Jeffrey Shallit, Mechanical Proofs of Properties of the Tribonacci Word, arXiv:1407.5841 [cs.FL], 2014.

H. Mousavi and J. Shallit, Mechanical Proofs of Properties of the Tribonacci Word, In: Manea F., Nowotka D. (eds) Combinatorics on Words. WORDS 2015. Lecture Notes in Computer Science, vol 9304. Springer, 2015, pp. 170-190.

Formula

a(n) = (A080843(n-1)-1)*(A080843(n-1)-2)/2. - Wolfdieter Lang, Dec 06 2018

Crossrefs

Cf. A003144, A080843, A276796.

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

Sequence in context: A162549 A191188 A285592 * A284364 A115788 A195062

Adjacent sequences: A276790 A276791 A276792 * A276794 A276795 A276796

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 28 2016

Extensions

Data and offset changed by Michel Dekking, Oct 12 2019

Status

approved