A395089 Binary complement of A395088.

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

Offset

0

Comments

Start with 1, apply 1 -> 100, 0 -> 1, take limit.

Define strings S(0) = 0, S(1) = 1, S(n) = S(n-1)S(n-2)S(n-2); iterate; sequence is S(infinity).

Related to the Thue-Morse sequence A010060 (see formula section).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10922

Formula

a(n) = 1 - A395088(n).

a(n) = A026465(n+2) - 1.

P(a(n) = 0) = P(a(n) = 1) = 1/2.

a(n) = A284391(n+2).

a(n) = A284388(n+3).

Example

100111001001001110011100111001001001110010010011...

Mathematica

f[n_]:=Module[{a={1}, b={0}}, While[Length[a]<n, {a, b}={Join[a, b, b], a}]; Take[a, n]]; a[n_]:=Module[{a={1}, b={0}}, While[Length[a]<=n, {a, b}={Join[a, b, b], a}]; a[[n+1]]]; a/@Range[0, 86] (* Robert P. P. McKone, Apr 14 2026 *)
(* Alternative: *)
First[SubstitutionSystem[{0 -> {1}, 1 -> {1, 0, 0}}, {1}, {7}]] (* Paolo Xausa, May 04 2026 *)

Prog

(Python)
def first(n): # returns first n terms
    f0, f1 = "10"
    while len(f0) < n:
        f0, f1 = f0+2*f1, f0
    return list(map(int, f0[0:n]))
print(first(87))

Crossrefs

Cf. A010060, A026465.

Cf. A003849, A005614, A171588, A080764, A395088.

Sequence in context: A057211 A120531 A106665 * A004609 A287674 A071001

Adjacent sequences: A395086 A395087 A395088 * A395090 A395091 A395092

Keyword

nonn,easy

Author

A.H.M. Smeets, Apr 11 2026

Status

approved