A286924 Positions of 1 in A286922; complement of A286923.

1, 2, 4, 5, 6, 8, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85

Offset

1,2

Comments

a(n) - a(n-1) is in {1,2} for n>=2, and a(n)/n -> 2 - sqrt(1/2).

Links

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

Formula

From Ridouane Oudra, Nov 02 2024: (Start)

a(n) = floor((n+1)*r - 1), where r = 2 - sqrt(1/2).

a(n) = 2*n - floor((n+1)/sqrt(2)).

a(n) = 2*n - A049472(n+1). (End)

Example

As a word, A286922 = 1101110111101110111101110..., in which 1 is in positions 1,2,4,5,6,8....

Maple

seq(floor((2-sqrt(1/2))*(n+1)-1), n=1..60); # Ridouane Oudra, Nov 02 2024

Mathematica

s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 7] (* A080764 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "01"}]
st = ToCharacterCode[w1] - 48 ; (* A286922 *)
Flatten[Position[st, 0]];  (* A286923 *)
Flatten[Position[st, 1]];  (* A286924 *)

Crossrefs

Cf. A080764, A286922, A286923, A049472.

Sequence in context: A285670 A030124 A064318 * A039100 A184482 A141204

Adjacent sequences: A286921 A286922 A286923 * A286925 A286926 A286927

Keyword

nonn,easy

Author

Clark Kimberling, May 17 2017

Status

approved