A368199 Number of times n appears as a term of A105774.

1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0

Offset

0,2

Comments

Although 0 is not a term of A105774, it makes sense to define A105774(0) = 0. Hence a(0) for this sequence is equal to 1.

Links

Table of n, a(n) for n=0..86.

Benoit Cloitre and Jeffrey Shallit, Some Fibonacci-Related Sequences, arXiv:2312.11706 [math.CO], 2023.

Formula

There is a 9-state Fibonacci automaton that, on input n in Fibonacci (Zeckendorf) representation, computes a(n). Rewritten as a morphism, {a(n)} is the infinite fixed point of the morphism 0->01, 1->2, 2->45, 3->67, 4->67, 5->8, 6->61, 7->6, 8->35, followed by the coding sending 4,6->0; 0,2,3,7->1; 1,5,8->2.

Crossrefs

Cf. A105774, A368200.

Sequence in context: A362450 A298731 A321102 * A091392 A036577 A317189

Adjacent sequences: A368196 A368197 A368198 * A368200 A368201 A368202

Keyword

nonn

Author

Jeffrey Shallit, Dec 16 2023

Status

approved