A285520 Positions of 1 in A285518; complement of A285519.

1, 2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 22, 24, 26, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 46, 48, 50, 52, 53, 54, 56, 58, 59, 60, 62, 64, 65, 66, 68, 70, 71, 72, 74, 76, 77, 78, 80, 82, 83, 84, 86, 88, 90, 92, 94, 96, 97, 98, 100, 102, 103

Offset

1,2

Comments

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

Proof of this conjecture: the limit equals 1/f1, where f1 is the frequency of 1 in (a(n)), and 1/f1 = phi = golden ratio. See A285519 for more details. - Michel Dekking, Feb 22 2021

Links

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

Example

As a word, A285518 = 11010111010111010111..., in which 1 is in positions 1,2,4,6,7,...

Mathematica

s = Nest[Flatten[# /. {0 -> {1, 1}, 1 -> {0, 0, 1, 1}}] &, {0}, 7] (* A285504 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"11" -> "1", "00" -> "0"}]
s1 = ToCharacterCode[w1] - 48 (* A285518 *)
Flatten[Position[s1, 0]]  (* A285519 *)
Flatten[Position[s1, 1]]  (* A285520 *)

Crossrefs

Cf. A285504, A285515, A285518, A285519.

Sequence in context: A153167 A227187 A047237 * A039028 A153282 A014661

Adjacent sequences: A285517 A285518 A285519 * A285521 A285522 A285523

Keyword

nonn,easy

Author

Clark Kimberling, Apr 30 2017

Status

approved