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.

A084524 Sequence A084523 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, 1110, 111, 10011, 1011, 1101, 111, 10011, 1101, 1110, 111, 10011, 11001, 1101, 111, 10011, 11001, 1110, 111, 100011, 10011, 1011, 111, 100011
Offset: 0

Views

Author

Antti Karttunen, Jun 02 2003

Keywords

Formula

a(n) = A007088(A084523(n)).

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

Views

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.

Links

Crossrefs

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

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.

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.

A084525 Partial sums of A084526.

Original entry on oeis.org

0, 1, 3, 6, 9, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265
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 A084521. Gives also the positions of 7s (ground states) in A084523.

Links

Crossrefs

Differs from A084515 first time at the 18th term, where A084515(18) = 64, while A084525(18) = 65. Cf. also A084505.

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.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.