A284772 Fixed point of the morphism 0 -> 01, 1 -> 0010.

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

Offset

1

Links

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

Jeffrey Shallit, Proof of Irvine's conjecture via mechanized guessing, arXiv preprint arXiv:2310.14252 [math.CO], revised version of November 24 2023.

Formula

a(n) = A286389(n-1) mod 2. - Jeffrey Shallit, Nov 27 2023

Example

0 -> 01-> 010010 -> 0100100101001001 -> ...

Mathematica

s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0, 0, 1, 0}}] &, {0}, 6] (* this sequence *)
Flatten[Position[s, 0]]  (* A284773 *)
Flatten[Position[s, 1]]  (* A284774 *)

Crossrefs

Cf. A284773, A284774, A286389.

Sequence in context: A305386 A174998 A257800 * A051069 A051065 A091445

Adjacent sequences: A284769 A284770 A284771 * A284773 A284774 A284775

Keyword

nonn,easy

Author

Clark Kimberling, Apr 13 2017

Status

approved