A334941 For any n > 0, let w be the least positive number such that the values (a(n+1-w), ..., a(n-1), e) do not appear continuously in (a(1), ..., a(n-1)) for some e in {0, 1}; a(n) is the least such e.

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

Offset

1

Comments

In other words, at each step we introduce a minimal suffix that has not yet appeared; we first minimize its length, and in case of a tie, we choose the lexicographically earliest.

Will every finite sequence of 0's and 1's appear?

Differs from A079101 for the first time at n = 70. - Jeffrey Shallit, Dec 14 2022

Links

Table of n, a(n) for n=1..87.

Rémy Sigrist, Pin plot of the number of 0's minus the number of 1's among the first n terms for n = 1..500000

Rémy Sigrist, Perl program for A334941

Example

For n = 1:
- for w = 1: (0) has not appeared,
- so a(1) = 0.
For n = 2:
- for w = 1: (0) has appeared but (1) has not,
- so a(2) = 1.
For n = 3:
- for w = 1: (0) and (1) have appeared,
- for w = 2: (1, 0) has not appeared,
- so a(3) = 0.
For n = 4:
- for w = 1: (0) and (1) have appeared,
- for w = 2: (0, 0) has not appeared,
- so a(4) = 0.
For n = 5:
- for w = 1: (0) and (1) have appeared,
- for w = 2: (0, 0) and (0, 1) have appeared,
- for w = 3: (0, 0, 0) has not appeared,
- so a(5) = 0.

Prog

(Perl) See Links section.

Crossrefs

Cf. A038219, A079101, A334944.

Sequence in context: A285831 A188294 A079101 * A076478 A091444 A091447

Adjacent sequences: A334938 A334939 A334940 * A334942 A334943 A334944

Keyword

nonn

Author

Rémy Sigrist, May 17 2020

Status

approved