A334944 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..w-1; a(n) is the least such e.

0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 2, 1, 1, 1, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 1, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 0, 1, 3, 0, 0, 0, 3, 1, 0, 0, 2, 1, 0, 0, 3, 0, 1, 0, 3, 2, 0, 0, 2, 2, 2, 0, 0, 3, 2, 1, 0, 1, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1

Offset

1,7

Comments

This sequence is an unbounded variant of A334941.

Will every finite sequence of nonnegative integers appear?

Links

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

Rémy Sigrist, Colored scatterplot of the ordinal transform of the first 1000000 terms

Rémy Sigrist, Perl program for A334944

Example

For n = 1:
- for w = 1: (0) did not appear,
- so a(1) = 0.
For n = 2:
- for w = 1: (0) appeared,
- for w = 2: (0, 0) did not appear,
- so a(2) = 0.
For n = 3:
- for w = 1: (0) appeared,
- for w = 2: (0, 0) appeared but (0, 1) did not,
- so a(3) = 1.

Prog

(Perl) See Links section.

Crossrefs

See A334941 and A334956 for similar sequences.

Sequence in context: A307666 A319995 A266344 * A174875 A193510 A353337

Adjacent sequences: A334941 A334942 A334943 * A334945 A334946 A334947

Keyword

nonn

Author

Rémy Sigrist, May 17 2020

Status

approved