A286031 Positions of 1 in A285568; complement of A285569.

1, 2, 4, 5, 8, 9, 11, 12, 13, 14, 16, 17, 20, 21, 23, 24, 26, 27, 30, 31, 33, 34, 36, 37, 40, 41, 43, 44, 45, 46, 48, 49, 52, 53, 55, 56, 58, 59, 62, 63, 66, 67, 70, 71, 73, 74, 76, 77, 80, 81, 83, 84, 85, 86, 88, 89, 92, 93, 95, 96, 98, 99, 102, 103, 105

Offset

1,2

Comments

Conjecture: a(n)/n -> (1+sqrt(5))/2 = golden ratio (A001622).

Proof of this conjecture: the limit is 1/f0 where f0 is the frequency of 0 in (a(n)). Since the generating morphism of (a(n)) has the same incidence matrix as the generating morphism 0->11, 1->0101 of the sequence A285518, it follows that 1/f0 = phi = golden ratio. - Michel Dekking, Feb 22 2021

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Example

As a word, A285568 = 110110011011..., in which 1 is in positions 1,2,4,5,8,...

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 1, 1, 0}}] &, {0}, 9] (* A285568 *)
Flatten[Position[s, 0]]  (* A285569 *)
Flatten[Position[s, 1]]  (* A286031 *)

Crossrefs

Cf. A001622, A285566, A285568, A285569.

Sequence in context: A267703 A277075 A038558 * A027883 A201818 A047380

Adjacent sequences: A286028 A286029 A286030 * A286032 A286033 A286034

Keyword

nonn,easy

Author

Clark Kimberling, Apr 30 2017

Status

approved