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.

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A084529 Number of 'prime' ground-state 3-ball juggling sequences of period n.

Original entry on oeis.org

1, 1, 3, 12, 42, 142, 502, 1702, 5878
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

This sequence counts the length n asynchronic site swaps given in A084521/A084522.
A juggling sequence is defined as 'prime', if it does not visit any state more than once. This means that in A084523 no integer occurs twice between consecutive sevens.

References

  • B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, pp. 50-51.

Links

Crossrefs

First differences of A084528. Cf. A084509, A084519.

A084451 Juggling states associated with the juggling sequence A084452.

Original entry on oeis.org

7, 11, 13, 14, 7, 19, 25, 28, 14, 7, 35, 21, 26, 13, 22, 11, 37, 50, 25, 44, 22, 11, 69, 38, 19, 41, 52, 26, 13, 70, 35, 49, 56, 28, 14, 7, 67, 97, 112, 56, 28, 14, 7, 131, 73, 100, 50, 25, 76, 38, 19, 137, 84, 42, 21, 74, 37, 82, 41, 148, 74, 37, 146, 73, 164, 82, 41, 276
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Positions of sevens (ground states): A084449. Same sequence in binary: A084451.

Formula

a(0)=7, a(n) = (A084451(n-1) + 2^A084452(n) - 1)/2.

A084452 An infinite juggling sequence with three balls: a(n) is zero when A084451(n-1) is even, otherwise the least (lowest) throw such that the resulting next juggling state A084451(n) does not occur in A084451[0..n-1].

Original entry on oeis.org

4, 4, 4, 0, 5, 5, 5, 0, 0, 6, 3, 5, 0, 5, 0, 6, 6, 0, 6, 0, 0, 7, 3, 0, 6, 6, 0, 0, 7, 0, 6, 6, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 8, 4, 7, 0, 0, 7, 0, 0, 8, 5, 0, 0, 7, 0, 7, 0, 8, 0, 0, 8, 0, 8, 0, 0, 9, 0, 0, 7, 0, 7, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, 9, 3, 0, 8, 1, 7, 0, 0, 0, 9, 0, 8, 8, 0, 0, 0, 0, 0, 9, 5, 8, 0
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Note that after the zero-throws the resulting next juggling state might be one encountered before. See A084458 for variant in which this does not happen.

Links

A084517 First occurrence of n in A084511.

Original entry on oeis.org

16, 6, 3, 1, 2, 7, 41, 210, 1014, 4677, 20779, 89800, 379952
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Cf. A084507, A084527.

A084527 First occurrence of n in A084521.

Original entry on oeis.org

16, 6, 3, 1, 2, 7, 37, 181, 799, 3503, 14365, 58033, 225215
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Cf. A084507, A084517.

A084449 Positions of sevens (ground states) in A084451.

Original entry on oeis.org

0, 4, 9, 35, 42, 101, 143, 365, 693, 729, 926, 1691, 1721, 2264, 2858, 3671, 4919, 7851, 8469, 8988, 11401, 12087, 15246, 21265, 21410, 28542, 30539, 35126, 40991, 49589, 51956, 59259, 68723, 86325, 89978, 106190, 114594, 122923, 143724, 150610
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

First differences: A084465.

Extensions

More terms from David Wasserman, Dec 30 2004

A084454 Inverse permutation to A084453.

Original entry on oeis.org

4, 1, 2, 3, 8, 9, 5, 6, 7, 13, 11, 15, 10, 12, 18, 14, 20, 21, 16, 17, 24, 19, 23, 27, 28, 22, 30, 25, 26, 33, 34, 35, 29, 31, 32, 39, 40, 41, 42, 36, 37, 38, 46, 47, 44, 49, 50, 43, 45, 53, 54, 48, 56, 52, 58, 51, 60, 61, 55, 63, 57, 65, 66, 59, 68, 69, 62, 71, 64, 73, 74, 75
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Used to compute A084455.

A084460 Inverse permutation to A084459.

Original entry on oeis.org

4, 1, 2, 7, 8, 3, 5, 11, 9, 13, 6, 15, 16, 10, 18, 12, 20, 21, 22, 14, 17, 25, 26, 27, 28, 19, 23, 31, 32, 29, 34, 35, 24, 37, 38, 39, 30, 41, 33, 43, 44, 45, 46, 36, 48, 40, 50, 51, 52, 53, 54, 42, 47, 57, 58, 59, 55, 61, 62, 49, 64, 65, 66, 67, 56, 69, 70, 60, 72, 73, 74, 75
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Used to compute A084461.

A084463 Positions of even juggling states in A084457, i.e., positions of zeros in A084458 - 1.

Original entry on oeis.org

3, 6, 7, 10, 12, 14, 15, 17, 19, 20, 21, 24, 25, 26, 27, 30, 31, 33, 34, 36, 37, 38, 40, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 82, 83, 84, 87, 88, 89, 91, 92, 93, 95, 96, 97, 98, 100, 101, 102
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Complement: A084464.

A084464 Positions of odd juggling states in A084457, i.e., positions of nonzero-throws in A084458 - 1.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 9, 11, 13, 16, 18, 22, 23, 28, 29, 32, 35, 39, 41, 46, 48, 54, 55, 59, 62, 67, 70, 76, 78, 85, 86, 90, 94, 99, 103, 109, 112, 119, 121, 129, 130, 139, 140, 145, 150, 156, 160, 167, 170, 178, 180, 189, 191, 201, 202, 208, 213, 220, 224, 232, 235, 244
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Complement: A084463. Used to compute A084467.
Previous Showing 31-40 of 51 results. Next

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