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 1-6 of 6 results.

A084526 The length of each successively larger, indecomposable, 'prime' 3-ball ground-state site swap given in A084521, i.e., the number of digits in each term of A084522.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

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Partial sums: A084525. Differs from A084516 first time at the 18th term, where A084516(18) = 4, while A084526(18) = 5. Cf. also A084506, A084520, A084528.

A084521 An infinite juggling sequence of three balls: successively larger 'prime' ground-state 3-ball site swaps listed in lexicographical order. A subset of A084511.

Original entry on oeis.org

3, 4, 2, 4, 4, 1, 5, 2, 2, 5, 3, 1, 4, 4, 4, 0, 4, 5, 3, 0, 5, 2, 4, 1, 5, 3, 4, 0, 5, 5, 1, 1, 5, 5, 2, 0, 6, 2, 2, 2, 6, 2, 3, 1, 6, 3, 1, 2, 6, 3, 3, 0, 6, 4, 1, 1, 6, 4, 2, 0, 4, 5, 5, 0, 1, 4, 6, 1, 3, 1, 4, 6, 4, 0, 1, 5, 2, 4, 4, 0, 5, 2, 5, 3, 0, 5, 3, 5, 0, 2, 5, 5, 1, 4, 0, 5, 5, 5, 0, 0, 5, 6, 1, 1, 2
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

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.

Examples

			The successive site swaps are: 3; 4,2; 4,4,1; 5,2,2; 5,3,1; 4,4,4,0; 4,5,3,0; ... See A084522.

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The number of such site swaps of length n is given by A084529. First position where n appears: A084527.

A084512 Successively larger 3-ball indecomposable ground-state site swaps of A084511 in concatenated decimal notation.

Original entry on oeis.org

3, 42, 441, 522, 531, 4440, 4512, 4530, 5241, 5340, 5511, 5520, 6222, 6231, 6312, 6330, 6411, 6420, 44502, 45141, 45501, 46122, 46131, 46302, 46401, 52440, 52512, 52530, 53502, 55140, 55500, 56112, 56130, 56202, 56400, 62241, 62340, 62511
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Note that this decimal representation works only up to the A084510(A084517(10))-1 = 2748th term which is 99600000, after which follows the 2749th solution 10,2,2,2,2,2,2,2 which would be usually represented as "A2222222".

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The number of terms of length n is given by A084519.
Subset of A084502. Cf. A084522.

A084502 Successively larger 3-ball ground-state site swaps of A084501 in concatenated decimal notation.

Original entry on oeis.org

3, 33, 42, 333, 342, 423, 441, 522, 531, 3333, 3342, 3423, 3441, 3522, 3531, 4233, 4242, 4413, 4440, 4512, 4530, 5223, 5241, 5313, 5340, 5511, 5520, 6222, 6231, 6312, 6330, 6411, 6420, 33333, 33342, 33423, 33441, 33522, 33531, 34233, 34242, 34413
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Note that this decimal representation works only up to the A084500(A084507(10))-1 = 7707th term which is 99600000, after which follows the 7708th solution 10,2,2,2,2,2,2,2 which would be usually represented as "A2222222".

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Crossrefs

The number of 'digits' in term a(n) is given by A084506.
The number of terms of length n is given by A084509.
Cf. A084512, A084522.

A084520 a(0)=0, after which each n occurs A084526(n) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Also minimum i such that A084525(i) >= n. Tells that the n-th throw (n>=1) in A084521 belongs to the a(n)-th lexicographical solution A084522(a(n)).

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Differs from A084510 first time at the 65th term, where A084510(65) = 19, while A084520(65) = 18. Cf. A084500.

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

Views

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.
Showing 1-6 of 6 results.

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