A286922 {0->01}-transform of the Sturmian word A080764.

1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1

Offset

1

Comments

A080764 = 1101101110110111011011011101..., and replacing each 0 by 01 gives

11011101111011101111011101110111..., in which the positions of 0 are given by A286923, and of 1, by A286924.

Links

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

Formula

a(n) = floor((n+1)*r) - floor((n+2)*r) + 1, where r = (3-sqrt(2))/7. - Ridouane Oudra, Nov 04 2024

Maple

r:=(3-sqrt(2))/7: seq(floor((n+1)*r)-floor((n+2)*r)+1, n=1..100); # Ridouane Oudra, Nov 04 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, A286923, A286924.

Sequence in context: A105234 A285599 A284386 * A285668 A267813 A323000

Adjacent sequences: A286919 A286920 A286921 * A286923 A286924 A286925

Keyword

nonn,easy

Author

Clark Kimberling, May 17 2017

Status

approved