A286666 Positions of 0 in A286665; complement of A286667.

1, 3, 6, 8, 11, 13, 15, 18, 20, 23, 25, 27, 30, 32, 35, 37, 40, 42, 44, 47, 49, 52, 54, 56, 59, 61, 64, 66, 69, 71, 73, 76, 78, 81, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 110, 112, 114, 117, 119, 122, 124, 126, 129, 131, 134, 136, 139, 141, 143, 146

Offset: 1

Author

Clark Kimberling, May 13 2017

Keywords

• nonn
• easy

Comments

a(n) - a(n-1) is in {2,3} for n>=2. Conjecture: a(n)/n -> 1 + sqrt(2).

This conjecture follows easily from the fact that (a(n)) is a Beatty sequence, see my comments in A286665. - Michel Dekking, Mar 11 2018

Numbers with no trailing 0's in their minimal representation in terms of the positive Pell numbers (A317204). - Amiram Eldar, Mar 16 2022

Examples

			As a word, A286665 = 010110101101010110101101..., in which 0 is in positions 1,3,6,8,11,...
		

Links

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

Crossrefs

Cf. A171588, A286665, A286667, A317204.

Programs

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 0, 1}, 1 -> {0}}] &, {0}, 6] (* A171588 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "01"}]
st = ToCharacterCode[w1] - 48 ; (* A286665 *)
p0 = Flatten[Position[st, 0]];  (* A286666 *)
p1 = Flatten[Position[st, 1]];  (* A286667 *)