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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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.

A084457 Juggling states associated with the juggling sequence A084458.

Original entry on oeis.org

7, 11, 13, 38, 19, 25, 140, 70, 35, 21, 74, 37, 82, 41, 276, 138, 69, 98, 49, 536, 268, 134, 67, 97, 2096, 1048, 524, 262, 131, 73, 548, 274, 137, 324, 162, 81, 1064, 532, 266, 133, 322, 161, 4176, 2088, 1044, 522, 261, 386, 193, 8288, 4144, 2072, 1036, 518, 259, 145
Offset: 0

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Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Same sequence in binary: A084456.
Terms that are odd: A084467.

Formula

a(0)=7, a(n) = (A084457(n-1) + 2^A084458(n) - 1)/2.

A084458 An infinite juggling sequence using three balls: a(n) is the least (lowest) throw needed to ensure that none of the juggling states A084457[n..n+A006519(n)-1] occurs in A084457[0..n-1].

Original entry on oeis.org

4, 4, 6, 0, 5, 8, 0, 0, 3, 7, 0, 7, 0, 9, 0, 0, 7, 0, 10, 0, 0, 0, 7, 12, 0, 0, 0, 0, 4, 10, 0, 0, 9, 0, 0, 11, 0, 0, 0, 9, 0, 13, 0, 0, 0, 0, 9, 0, 14, 0, 0, 0, 0, 0, 5, 12, 0, 0, 0, 11, 0, 0, 14, 0, 0, 0, 0, 11, 0, 0, 15, 0, 0, 0, 0, 0, 10, 0, 16, 0, 0, 0, 0, 0, 0, 5, 13, 0, 0, 0, 13, 0, 0, 0, 15, 0, 0, 0
Offset: 1

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Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

The condition is equivalent to that A000265(A084457(n)) does not occur in A084457[0..n-1].

Links

Crossrefs

Variant: A084452. Positions of zeros, minus one: A084463.

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.

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

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

Views

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".

Links

Crossrefs

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

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.

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.

A084516 The length of each successively larger, indecomposable 3-ball ground-state site swap given in A084511, i.e., the number of digits in each term of A084512.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 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, 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
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Links

Crossrefs

Partial sums: A084515. Differs from A084526 first time at the 18th term, where A084516(18) = 4, while A084526(18) = 5. Cf. also A084506, A084510, A084518.

A084522 Successively larger 3-ball 'prime' ground-state site swaps of A084521 in concatenated decimal notation.

Original entry on oeis.org

3, 42, 441, 522, 531, 4440, 4530, 5241, 5340, 5511, 5520, 6222, 6231, 6312, 6330, 6411, 6420, 45501, 46131, 46401, 52440, 52530, 53502, 55140, 55500, 56112, 56130, 56202, 56400, 62241, 62340, 62511, 62520, 63141, 63501, 64140, 64500, 66111
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Comments

Note that this decimal representation works only up to the A084520(A084527(10))-1 = 1919th term which is 99600000, after which follows the 1920th solution 10,2,2,2,2,2,2,2 which would be usually represented as "A2222222".

Links

Crossrefs

The number of terms of length n is given by A084529. Subset of A084512.
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