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.

A084504 Sequence A084503 in binary.

Original entry on oeis.org

111, 111, 111, 111, 1011, 111, 111, 111, 111, 111, 1011, 111, 1011, 111, 111, 1011, 1101, 111, 10011, 1011, 111, 10011, 1101, 111, 111, 111, 111, 111, 111, 111, 1011, 111, 111, 1011, 111, 111, 111, 1011, 1101, 111, 111, 10011, 1011, 111, 111, 10011
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Formula

a(n) = A007088(A084503(n)).

A084501 An infinite juggling sequence of three balls: successively larger ground-state 3-ball site swaps listed in lexicographic order.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Every possible 3-ball asynchronic site swap of finite period occurs as a subsequence of this sequence. E.g., "51" (three-ball shower) occurs first time at a(65)=5, a(66)=1.
We obtain the sequence by traversing each possible loop of successively larger lengths in 3-ball state graph as depicted in Polster's book, or section 7 of Knutson's Siteswap FAQ (but not limited by throw height), starting from and ending to the ground state 7 (xxx) and by concatenating those sequences in lexicographic order.
One can take any subsequence A084501[i..j] such that A084503(i-1) = A084503(j) = 7 and try to juggle it periodically or give it to one of the Siteswap animators available at J.I.S., e.g., by taking the first 39 terms, one gets a site swap pattern "333423333424234415225313333334234233441".

Examples

			The successive site swaps are: 3; 3,3; 4,2; 3,3,3; 3,4,2; 4,2,3; 4,4,1; 5,2,2; 5,3,1; 3,3,3,3; ... See A084502.

References

  • B. Polster, The Mathematics of Juggling, Springer-Verlag, 2003, p. 45.

Links

Crossrefs

Subsets: A084511, A084521.
The number of such site swaps of length n is given by A084509.
First position where n appears: A084507.

A084523 Juggling states associated with the juggling sequence A084521.

Original entry on oeis.org

7, 7, 11, 7, 11, 13, 7, 19, 11, 7, 19, 13, 7, 11, 13, 14, 7, 11, 21, 14, 7, 19, 11, 13, 7, 19, 13, 14, 7, 19, 25, 13, 7, 19, 25, 14, 7, 35, 19, 11, 7, 35, 19, 13, 7, 35, 21, 11, 7, 35, 21, 14, 7, 35, 25, 13, 7, 35, 25, 14, 7, 11, 21, 26, 13, 7, 11, 37, 19, 13, 7, 11, 37, 26, 13, 7
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Same sequence in binary: A084524.
Cf. A084503, A084513.

Formula

a(0)=7, a(n) = (A084523(n-1) + 2^A084521(n) - 1)/2.

A084505 Partial sums of A084506.

Original entry on oeis.org

0, 1, 3, 5, 8, 11, 14, 17, 20, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 124, 129, 134, 139, 144, 149, 154, 159, 164, 169, 174, 179, 184, 189, 194, 199, 204, 209, 214, 219, 224, 229, 234, 239, 244, 249
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

For n>=1, (a(n-1)+1,a(n)) = (1,1),(2,3),(4,5),(6,8),(9,11),(12,14),... gives the starting and ending offsets of the n-th site swap in the sequence A084501.
Note: this sequence is related to juggling with three objects. For a similar sequence related to (ordinary) permutations, see A084555.

Links

Crossrefs

Differs from A084555 first time at the 130th term, where A084505(130) = 605, while A084555(130) = 604.
A084503(a(n)) = 7 for all n. However, this does not give the positions of all 7s in A084503 because the state sequences are not all indecomposable. Cf. A084515, A084525.

Extensions

Added the b-file, moved the misplaced Mathematica code to A084555, where it belongs. - Antti Karttunen, Oct 24 2012

A084513 Juggling states associated with the juggling sequence A084511.

Original entry on oeis.org

7, 7, 11, 7, 11, 13, 7, 19, 11, 7, 19, 13, 7, 11, 13, 14, 7, 11, 21, 11, 7, 11, 21, 14, 7, 19, 11, 13, 7, 19, 13, 14, 7, 19, 25, 13, 7, 19, 25, 14, 7, 35, 19, 11, 7, 35, 19, 13, 7, 35, 21, 11, 7, 35, 21, 14, 7, 35, 25, 13, 7, 35, 25, 14, 7, 11, 13, 22, 11, 7, 11, 21, 11, 13, 7, 11
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Same sequence in binary: A084514.
Cf. A084503, A084511, A084523.

Formula

a(0)=7, a(n) = (A084513(n-1) + 2^A084511(n) - 1)/2.
Showing 1-5 of 5 results.

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