cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A079101 A repetition-resistant sequence.

Original entry on oeis.org

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, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2003

Keywords

Comments

a(n) = 0 or 1, chosen so as to maximize the number of different subsequences that are formed.
a(n+1)=1 if and only if (a(1),a(2),...,a(n),0), but not (a(1),a(2),...,a(n),1), has greater length of longest repeated segment than (a(1),a(2),...,a(n)) has.
In Feb, 2003, Alejandro Dau solved Problem 3 on the Unsolved Problems and Rewards website, thus establishing that every binary word occurs infinitely many times in this sequence.
Klaus Sutmer remarks (Jun 26 2006) that this sequence is very similar to the Ehrenfeucht-Mycielski sequence A007061. Both sequences have every finite binary word as a factor; in fact, essentially the same proof works for both sequences.
Differs from A334941 for the first time at n = 70. - Jeffrey Shallit, Dec 14 2022

Examples

			a(7)=1 because (0,1,0,0,0,1,0) has repeated segment (0,1,0) of length 3, whereas (0,1,0,0,0,1,1) has no repeated segment of length 3.

Links

Crossrefs

Cf. A079136, A079335, A079336, A079337, A079338, A007061, A334941.

A079335 Positions of 1 in the repetition-resistant sequence A079101.

Original entry on oeis.org

2, 6, 7, 9, 11, 12, 13, 16, 19, 20, 21, 22, 24, 25, 31, 33, 38, 39, 40, 42, 45, 47, 48, 50, 51, 52, 53, 54, 58, 66, 67, 71, 72, 73, 74, 75, 76, 78, 80, 83, 84, 87, 89, 91, 93, 94, 97, 98, 100, 101, 103, 107, 109, 110, 111, 112, 115, 116, 117, 122, 125, 129, 132, 133, 135
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2003

Keywords

Comments

Complement of A079136.

Crossrefs

Cf. A079101, A079136, A079336, A079337, A079338.

A079336 A repetition-resistant sequence.

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 03 2003

Keywords

Comments

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

Examples

			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.

Links

Crossrefs

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

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.

A079337 Positions of 0 in the repetition-resistant sequence A079336.

Original entry on oeis.org

1, 4, 5, 7, 12, 14, 15, 16, 20, 21, 22, 23, 25, 26, 29, 32, 34, 37, 38, 39, 41, 43, 45, 46, 48, 49, 50, 51, 52, 55, 56, 64, 70, 71, 74, 75, 76, 77, 78, 79, 81, 84, 88, 91, 92, 95, 97, 99, 106, 107, 108, 114, 116, 120, 122, 124, 125, 126, 128, 132, 133, 137, 141, 142, 143
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2003

Keywords

Comments

Complement of A079338.

Crossrefs

Cf. A079101, A079136, A079335, A079336, A079338.

A079338 Positions of 1 in the repetition-resistant sequence A079336.

Original entry on oeis.org

2, 3, 6, 8, 9, 10, 11, 13, 17, 18, 19, 24, 27, 28, 30, 31, 33, 35, 36, 40, 42, 44, 47, 53, 54, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 72, 73, 80, 82, 83, 85, 86, 87, 89, 90, 93, 94, 96, 98, 100, 101, 102, 103, 104, 105, 109, 110, 111, 112, 113, 115, 117, 118, 119
Offset: 1

Views

Author

Clark Kimberling, Jan 03 2003

Keywords

Comments

Complement of A079337.

Crossrefs

Cf. A079101, A079136, A079335, A079336, A079337.
Showing 1-5 of 5 results.

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