A283966 Fixed point of the morphism 0 -> 1, 1 -> 10101.

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

Offset

1

Comments

Let u(n) = # 0's <= n and v(n) = # 1's <= n. Let r = (7+sqrt(17))/4 and s = (-1+sqrt(17))/2, so that 1/r + 1/s = 1. Conjecture: -1 < n*r - u(n) < 3 and -1 < n*s - v(n) < 2 for n >= 1.

Links

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

Index entries for sequences that are fixed points of mappings

Example

1 -> 10101 -> 10101110101110101 -> ...

Mathematica

s = Nest[Flatten[# /. {0 -> {1}, 1 -> {1, 0, 1, 0, 1}}] &, {0}, 10] (* A283966 *)
Flatten[Position[s, 0]]  (* A283967 *)
Flatten[Position[s, 1]]  (* A284015 *)
SubstitutionSystem[{0->{1}, 1->{1, 0, 1, 0, 1}}, {1}, {5}][[1]] (* Harvey P. Dale, Mar 24 2022 *)

Crossrefs

Cf. A283967, A284015.

Sequence in context: A245656 A354032 A285625 * A054354 A156728 A361023

Adjacent sequences: A283963 A283964 A283965 * A283967 A283968 A283969

Keyword

nonn,easy

Author

Clark Kimberling, Mar 26 2017

Status

approved