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.

A084514 Sequence A084513 in binary.

Original entry on oeis.org

111, 111, 1011, 111, 1011, 1101, 111, 10011, 1011, 111, 10011, 1101, 111, 1011, 1101, 1110, 111, 1011, 10101, 1011, 111, 1011, 10101, 1110, 111, 10011, 1011, 1101, 111, 10011, 1101, 1110, 111, 10011, 11001, 1101, 111, 10011, 11001, 1110, 111, 100011
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

Keywords

Formula

a(n) = A007088(A084513(n)).

A084511 An infinite juggling sequence of three balls: successively larger indecomposable ground-state 3-ball site swaps listed in lexicographical order. A subset of A084501.

Original entry on oeis.org

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

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

By "indecomposable" we mean that the juggling state sequence associated to each loop should not return to the ground state 7 (xxx) until after the last throw. I.e., this means that A084515 gives positions of ALL the 7s (ground states) in A084513.
One can take any subsequence A084511[A084515(i)+1..A084515(j)] (j>i) 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 terms 4-12, one gets a site swap pattern "441522531".

Examples

			The successive site swaps are: 3; 4,2; 4,4,1; 5,2,2; 5,3,1; 4,4,4,0; 4,5,1,2; 4,5,3,0; ... See A084512.

Links

Crossrefs

Subset: A084521.
The number of such site swaps of length n is given by A084519.
First position where n appears: A084517.

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

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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.

A084503 Binary juggling state vectors (given in decimal), associated with the three balls juggling sequence A084501.

Original entry on oeis.org

7, 7, 7, 7, 11, 7, 7, 7, 7, 7, 11, 7, 11, 7, 7, 11, 13, 7, 19, 11, 7, 19, 13, 7, 7, 7, 7, 7, 7, 7, 11, 7, 7, 11, 7, 7, 7, 11, 13, 7, 7, 19, 11, 7, 7, 19, 13, 7, 11, 7, 7, 7, 11, 7, 11, 7, 11, 13, 7, 7, 11, 13, 14, 7, 11, 21, 11, 7, 11, 21, 14, 7, 19, 11, 7, 7, 19, 11, 13, 7, 19, 13, 7, 7, 19
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Same sequence in binary: A084504.
Cf. A084513, A084523.
A084468 gives the records.

Formula

a(0)=7, a(n)=(A084503(n-1)+(2^A084501(n))-1)/2.

A084515 Partial sums of A084516.

Original entry on oeis.org

0, 1, 3, 6, 9, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 69, 74, 79, 84, 89, 94, 99, 104, 109, 114, 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, 254, 259, 264, 269
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

For n>=1, (a(n-1)+1,a(n)) = (1,1),(2,3),(4,6),(7,9),(10,12),... gives the starting and ending offsets of the n-th site swap in the sequence A084511. Gives also the positions of 7s (ground states) in A084513.

Links

Crossrefs

Differs from A084525 first time at the 18th term, where A084515(18) = 64, while A084525(18) = 65.
Cf. also A084505.
Showing 1-5 of 5 results.

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