A079336 A repetition-resistant sequence.

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

Offset

1,1

Comments

Unsolved problem: is every finite binary sequence a segment of a?

Links

Table of n, a(n) for n=1..105.

Clark Kimberling, Unsolved Problems and Rewards.

Clark Kimberling, Problem 2289, Crux Mathematicorum 23 (1997) 501.

Formula

a(n+1)=0 if and only if (a(1), a(2), ..., a(n), 1), but not (a(1), a(2), ..., a(n), 0), has greater length of longest repeated segment than (a(1), a(2), ..., a(n)) has.

Example

a(8)=1 because (0,1,1,0,0,1,0,0) has repeated segment (1,0,0) of length 3, whereas (0,1,1,0,0,1,0,1) has no repeated segment of length 3.

Crossrefs

Cf. A079101, A079136, A079335, A079337, A079338.

Sequence in context: A286049 A287657 A347198 * A288670 A057215 A284905

Adjacent sequences: A079333 A079334 A079335 * A079337 A079338 A079339

Keyword

nonn

Author

Clark Kimberling, Jan 03 2003

Status

approved