A084458 -id:A084458 - cp's OEIS frontend

A084461 Permutation of Z, obtained by reflecting the juggling sequence A084458 from positive to negative numbers (with zero thrown at beat 0), folded to N with functions N2Z and Z2N.

1, 10, 2, 12, 4, 18, 6, 8, 9, 20, 3, 28, 5, 14, 15, 16, 17, 24, 7, 34, 11, 22, 23, 38, 19, 26, 27, 46, 13, 30, 31, 32, 33, 48, 21, 36, 37, 58, 25, 40, 41, 42, 43, 44, 45, 60, 29, 72, 35, 50, 51, 52, 53, 54, 55, 56, 57, 66, 39, 80, 47, 62, 63, 64, 65, 84, 59, 68, 69, 70, 71, 94

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

This permutation consists of three infinite cycles + infinite number of fixed points.

Inverse: A084462. Cf. also A084460, A084455, A084491, A084495, A084499, A065166.

[seq(Z2N(A084461_Z2Z(N2Z(n))),n=1..45)];
N2Z := n -> ((-1)^n)*floor(n/2);
Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);
A084461_Z2Z := z -> z+`if`((z > 0), A084458(z),`if`((z >= -3),2*(-z), A084458(A084460((-z)-3))));

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

Antti Karttunen, Jun 02 2003

nonn

A. Karttunen, Scheme-program for computing this sequence

Same sequence in binary: A084456.

Terms that are odd: A084467.

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

A084459 a(n) = n + A084458(n) - 3.

Original entry on oeis.org

2, 3, 6, 1, 7, 11, 4, 5, 9, 14, 8, 16, 10, 20, 12, 13, 21, 15, 26, 17, 18, 19, 27, 33, 22, 23, 24, 25, 30, 37, 28, 29, 39, 31, 32, 44, 34, 35, 36, 46, 38, 52, 40, 41, 42, 43, 53, 45, 60, 47, 48, 49, 50, 51, 57, 65, 54, 55, 56, 68, 58, 59, 74, 61, 62, 63, 64, 76, 66, 67, 83, 69

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

Inverse: A084460.

Cf. A084461, A084453, A084489, A084493, A084497.

A084463 Positions of even juggling states in A084457, i.e., positions of zeros in A084458 - 1.

Original entry on oeis.org

3, 6, 7, 10, 12, 14, 15, 17, 19, 20, 21, 24, 25, 26, 27, 30, 31, 33, 34, 36, 37, 38, 40, 42, 43, 44, 45, 47, 49, 50, 51, 52, 53, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 82, 83, 84, 87, 88, 89, 91, 92, 93, 95, 96, 97, 98, 100, 101, 102

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

Antti Karttunen, Scheme-program for computing this sequence

Complement: A084464.

A084464 Positions of odd juggling states in A084457, i.e., positions of nonzero-throws in A084458 - 1.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 9, 11, 13, 16, 18, 22, 23, 28, 29, 32, 35, 39, 41, 46, 48, 54, 55, 59, 62, 67, 70, 76, 78, 85, 86, 90, 94, 99, 103, 109, 112, 119, 121, 129, 130, 139, 140, 145, 150, 156, 160, 167, 170, 178, 180, 189, 191, 201, 202, 208, 213, 220, 224, 232, 235, 244

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

Antti Karttunen, Scheme-program for computing this sequence

Complement: A084463. Used to compute A084467.

A084452 An infinite juggling sequence with three balls: a(n) is zero when A084451(n-1) is even, otherwise the least (lowest) throw such that the resulting next juggling state A084451(n) does not occur in A084451[0..n-1].

Original entry on oeis.org

4, 4, 4, 0, 5, 5, 5, 0, 0, 6, 3, 5, 0, 5, 0, 6, 6, 0, 6, 0, 0, 7, 3, 0, 6, 6, 0, 0, 7, 0, 6, 6, 0, 0, 0, 7, 7, 7, 0, 0, 0, 0, 8, 4, 7, 0, 0, 7, 0, 0, 8, 5, 0, 0, 7, 0, 7, 0, 8, 0, 0, 8, 0, 8, 0, 0, 9, 0, 0, 7, 0, 7, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, 9, 3, 0, 8, 1, 7, 0, 0, 0, 9, 0, 8, 8, 0, 0, 0, 0, 0, 9, 5, 8, 0

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

Note that after the zero-throws the resulting next juggling state might be one encountered before. See A084458 for variant in which this does not happen.

Index entries for sequences related to juggling
A. Karttunen, Scheme-program for computing this sequence
A. Knutson, Siteswap FAQ, Section 7, A deeper level: landing schedules, or juggling states

cp's OEIS Frontend

A084461 Permutation of Z, obtained by reflecting the juggling sequence A084458 from positive to negative numbers (with zero thrown at beat 0), folded to N with functions N2Z and Z2N.

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Maple

A084457 Juggling states associated with the juggling sequence A084458.

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Formula

A084459 a(n) = n + A084458(n) - 3.

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A084463 Positions of even juggling states in A084457, i.e., positions of zeros in A084458 - 1.

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A084464 Positions of odd juggling states in A084457, i.e., positions of nonzero-throws in A084458 - 1.

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A084452 An infinite juggling sequence with three balls: a(n) is zero when A084451(n-1) is even, otherwise the least (lowest) throw such that the resulting next juggling state A084451(n) does not occur in A084451[0..n-1].

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